user7579: Recently, we've had two questions on Avatar: The Last Airbender and Legend of Korra which garnered close votes: Is avatar Korra bisexual? and How can fans be used to augment earthbending?. The first question has yet to receive the fifth vote necessary to close it. The second was closed, but later reopened. Looking at the edit history, the intersection of the group that voted to close and the group that voted to reopen is empty—so we had five users who thought the question was off-topic, and another five who thought it was on-topic. All ten of the users who voted on this are respected, high-rep users with lots of good contributions to the site, which suggests there is a pretty deep gulf over this issue in the community.
A previous meta post established that peripheral topics like Last Airbender, Korra, and RWBY are on-topic here, as well as allowing manhwa, manhua, original English language manga, and certain video games. This ruling was reinforced in another meta post on RWBY specifically, and in this duplicate of the first post. However, some users evidently were either not aware of these posts, or disagreed with them, and have been voting to close Last Airbender and Korra questions.
Do we still want to accept questions on these shows?
I do not want to start another argument about whether these two shows are anime or not. To me, they are not anime under the commonly understood definition in the non-Japanese fandom. To me, any work in which the vast majority of the creative direction comes from non-Japanese sources is not anime. However, Final Fantasy is also not anime, and we allow Final Fantasy questions, so not being anime is not an automatic disqualification. We can argue in circles about whether the shows qualify as anime under someone's definition, but it never goes anywhere. Let's try to focus on practical policy instead of arguing over definitions and gut feelings.

user1908: I personally see nothing wrong with prohibiting these questions here, since all three still have a home on SF&F (all three series in question are fantasy, and AtLA/Korra in particular have a much larger userbase over there) and AtLA/Korra also are certainly welcome on M&TV (dunno about RWBY). 
I am well aware that SE sites need not have mutually exclusive domains, but since this particular set of topics is controversial over here and uncontroversial on SF&F/M&TV, I think it makes our lives easier and nobody's lives harder if we just opt to migrate all new non-terrible AtLA/Korra/RWBY questions to SF&F or M&TV, as appropriate. (We can let existing questions be, or maybe just close them if ever they get bumped back to the front page.)

user7579: This is a consensus answer which details a policy on Western anime-inspired works that seems to be agreeable to all who answered or commented here.
For Questioners
Questions on Avatar: The Last Airbender and Legend of Korra are officially tolerated as on-topic on Anime and Manga Stack Exchange. You may ask questions on these series here. However, you are strongly encouraged to instead ask these questions on Sci-fi and Fantasy Stack Exchange, where there is a thriving community of experts on these series. You may also consider asking them on Movies & TV Stack Exchange. 
Questions about the live action Last Airbender movie are off-topic here, but on-topic at Sci-fi and Fantasy, as well as Movies and TV.
If, after posting your question, you decide you would rather have it on one of the other sites, please flag it for moderator attention. Choose the reason "Other (in need of moderator attention)" and mention in the message which site you would like the question migrated to.
This policy should not be taken to imply that Avatar: The Last Airbender and Legend of Korra are, or are not, anime. 
For Reviewers
Questions on Avatar: The Last Airbender and Legend of Korra should be held to the same standards as any other question. They should be clear, reasonable in scope, and answerable with facts and informed speculation rather than pure opinion. Downvote, edit, and vote to close or reopen these questions according to the same standards you would apply to any other question.
Please don't vote to close solely because the question is about Avatar: The Last Airbender or Legend of Korra on the basis that these shows are not anime. By looking over the question statement, answers, and comments on this page, you can see that several of us who participated in this discussion do not believe Avatar: The Last Airbender and Legend of Korra are anime. However, the community has historically decided to allow questions on certain topics which are not explicitly anime or unambiguously connected to anime. Please respect that choice, or argue for a change in policy in Meta before voting to close. 
You can, per above, encourage questioners to migrate their question to Sci-fi and Fantasy SE. You can also flag it for migration on the questioner's behalf, especially in cases where the questioner is a new user and doesn't understand the system very well.
For the Community
This site was created to be a Q&A site on Japanese anime and manga, as commonly understood by non-Japanese fans of these media. The definition of these terms is somewhat nebulous, but in general, a work is only unambiguously anime or manga if it was made in Japan, under the direct and extensive creative control of Japanese people. 
We've decided to allow questions on certain topics that fall outside of this definition because they are of interest to the community, and because they fall into a grey area in which one can argue that they are "close enough" to anime or "statistically anime" or fall inside the "anime-o-sphere". However, we are not going to become "East Asian-style Media Stack Exchange". If questions on these topics ever threaten to overwhelm questions on the core interests of the community, the policy will be reassessed and the topics may be banned.

user7579: I'll present my own take on the issue, but I welcome other opinions.
As I said in the question, to me, Last Airbender and Korra are not anime, but this should not mean automatic disqualification. Toshinou-san's answer presents a good case for why they should be allowed despite not being anime.
Questions on Last Airbender and Legend of Korra are on-topic at Sci Fi and Fantasy Stack Exchange. From looking over their tag list, there are 110 questions tagged avatar-the-last-airbender and 105 questions tagged legend-of-korra. They're also on-topic on Movies and TV Stack Exchange, with one question each. We won't be leaving anyone out in the cold by refusing these questions.
I think we should encourage anyone who asks a question on these two series here to move their question to Sci-Fi and Fantasy. Although there is definitely crossover in expertise, the majority of Stack Exchange users who are interested in these shows seem to have settled on Sci Fi and Fantasy as their chosen site. As Esq points out in a comment here, it's more important to congregate all the questions in one place than it is to argue philosophy:

Anyways whatever the choice is I think avatar should not be split up
  into 2 places, all current Q&A should be moved to a single place.
  Consistency is more important than being right in this case

Having all the questions in one place means it's easier to find out if your question has already been asked, and it's easier for answerers to find your question since they don't have to check three different sites. Whether or not you think Avatar is anime, the fact is that most of the questions on the show are on SFF.SE, while most of the questions on Full Metal Alchemist and Dragon Ball Z (which are also on-topic on both sites) are over here.
I'm not sure I favor closing any questions on Last Airbender or Korra. I think if we had never decided to take them, it would have been viable to close them as they come in. But at this point, we've already had a policy of allowing them for a while. And it's probably confusing for people to figure out whether they're allowed or not. I'd rather strongly encourage people to move their questions to SFF, with migration as a possibility. Perhaps we could also migrate all currently open questions on these topics, and make it clear in our tag wiki that the tags should not be used for new questions.

user1530: Personally I think they should be allowed.
These are as tangentally related to our userbase as other non-strictly-anime items that we allow are - like manwha. Clearly the userbase is interested in Avatar questions based on how many votes it got.
As for overlapping content, we have many questions about the plots of games - and there's an entire stack site for that.
I think it is fair enough that questions on works that are commonly associated with anime (even though they may not be) are of value to the community because of this status.
Whilst we shouldn't explicitly encourage these questions, I don't think that they shouldn't belong here.

7579: <p>Recently, we've had two questions on Avatar: The Last Airbender and Legend of Korra which garnered close votes: <a href="https://anime.stackexchange.com/q/24013/7579">Is avatar Korra bisexual?</a> and <a href="https://anime.stackexchange.com/q/19921/2604">How can fans be used to augment earthbending?</a>. The first question has yet to receive the fifth vote necessary to close it. The second was closed, but later reopened. Looking at the <a href="https://anime.stackexchange.com/posts/19921/revisions">edit history</a>, the intersection of the group that voted to close and the group that voted to reopen is empty&mdash;so we had five users who thought the question was off-topic, and another five who thought it was on-topic. All ten of the users who voted on this are respected, high-rep users with lots of good contributions to the site, which suggests there is a pretty deep gulf over this issue in the community.</p>

<p><a href="https://anime.meta.stackexchange.com/q/415/7579">A previous meta post</a> established that peripheral topics like Last Airbender, Korra, and RWBY are on-topic here, as well as allowing manhwa, manhua, original English language manga, and certain video games. This ruling was reinforced in <a href="https://anime.meta.stackexchange.com/a/840/7579">another meta post</a> on RWBY specifically, and in <a href="https://anime.meta.stackexchange.com/q/2385/7579">this duplicate</a> of the first post. However, some users evidently were either not aware of these posts, or disagreed with them, and have been voting to close Last Airbender and Korra questions.</p>

<p>Do we still want to accept questions on these shows?</p>

<p>I <em>do not</em> want to start another argument about whether these two shows are anime or not. To me, they are not anime under the commonly understood definition in the non-Japanese fandom. To me, any work in which the vast majority of the creative direction comes from non-Japanese sources is not anime. However, Final Fantasy is also not anime, and we allow Final Fantasy questions, so not being anime is not an automatic disqualification. We can argue in circles about whether the shows qualify as anime under someone's definition, but it never goes anywhere. Let's try to focus on practical policy instead of arguing over definitions and gut feelings.</p>
 1908: <p>I personally see nothing wrong with prohibiting these questions here, since all three still have a home on SF&amp;F (all three series in question are fantasy, and AtLA/Korra in particular have a much larger userbase over there) and AtLA/Korra also are certainly welcome on M&amp;TV (dunno about RWBY). </p>

<p>I am well aware that SE sites need not have mutually exclusive domains, but since this particular set of topics is controversial over here and uncontroversial on SF&amp;F/M&amp;TV, I think it makes our lives easier and nobody's lives harder if we just opt to migrate all new non-terrible AtLA/Korra/RWBY questions to SF&amp;F or M&amp;TV, as appropriate. (We can let existing questions be, or maybe just close them if ever they get bumped back to the front page.)</p>
 7579: <p>This is a consensus answer which details a policy on Western anime-inspired works that seems to be agreeable to all who answered or commented here.</p>

<h1>For Questioners</h1>

<p>Questions on Avatar: The Last Airbender and Legend of Korra are officially tolerated as on-topic on Anime and Manga Stack Exchange. You may ask questions on these series here. However, you are strongly encouraged to instead ask these questions on <a href="http://scifi.stackexchange.com">Sci-fi and Fantasy Stack Exchange</a>, where there is a thriving community of experts on these series. You may also consider asking them on <a href="http://movies.stackexchange.com">Movies &amp; TV Stack Exchange</a>. </p>

<p>Questions about the live action Last Airbender movie are off-topic here, but on-topic at Sci-fi and Fantasy, as well as Movies and TV.</p>

<p>If, after posting your question, you decide you would rather have it on one of the other sites, please flag it for moderator attention. Choose the reason "Other (in need of moderator attention)" and mention in the message which site you would like the question migrated to.</p>

<p>This policy should not be taken to imply that Avatar: The Last Airbender and Legend of Korra are, or are not, anime. </p>

<h1>For Reviewers</h1>

<p>Questions on Avatar: The Last Airbender and Legend of Korra should be held to <a href="https://anime.stackexchange.com/help/closed-questions">the same standards as any other question</a>. They should be clear, reasonable in scope, and answerable with facts and informed speculation rather than pure opinion. Downvote, edit, and vote to close or reopen these questions according to the same standards you would apply to any other question.</p>

<p>Please don't vote to close solely because the question is about Avatar: The Last Airbender or Legend of Korra on the basis that these shows are not anime. By looking over the question statement, answers, and comments on this page, you can see that several of us who participated in this discussion do not believe Avatar: The Last Airbender and Legend of Korra are anime. However, the community has historically decided to allow questions on certain topics which are not explicitly anime or unambiguously connected to anime. Please respect that choice, or argue for a change in policy in Meta before voting to close. </p>

<p>You <em>can</em>, per above, encourage questioners to migrate their question to Sci-fi and Fantasy SE. You can also flag it for migration on the questioner's behalf, especially in cases where the questioner is a new user and doesn't understand the system very well.</p>

<h1>For the Community</h1>

<p>This site was created to be a Q&amp;A site on Japanese anime and manga, as commonly understood by non-Japanese fans of these media. The definition of these terms is somewhat nebulous, but in general, a work is only unambiguously anime or manga if it was made in Japan, under the direct and extensive creative control of Japanese people. </p>

<p>We've decided to allow questions on certain topics that fall outside of this definition because they are of interest to the community, and because they fall into a grey area in which one can argue that they are "close enough" to anime or "statistically anime" or fall inside the "anime-o-sphere". However, we are not going to become "East Asian-style Media Stack Exchange". If questions on these topics ever threaten to overwhelm questions on the core interests of the community, the policy will be reassessed and the topics may be banned.</p>
 7579: <p>I'll present my own take on the issue, but I welcome other opinions.</p>

<p>As I said in the question, to me, Last Airbender and Korra are not anime, but this should not mean automatic disqualification. <a href="https://anime.meta.stackexchange.com/a/2530/7579">Toshinou-san's answer</a> presents a good case for why they should be allowed despite not being anime.</p>

<p>Questions on Last Airbender and Legend of Korra are on-topic at Sci Fi and Fantasy Stack Exchange. From looking over their tag list, there are 110 questions tagged <a href="https://anime.stackexchange.com/questions/tagged/avatar-the-last-airbender" class="post-tag" title="show questions tagged &#39;avatar-the-last-airbender&#39;" rel="tag">avatar-the-last-airbender</a> and 105 questions tagged <a href="https://anime.stackexchange.com/questions/tagged/legend-of-korra" class="post-tag" title="show questions tagged &#39;legend-of-korra&#39;" rel="tag">legend-of-korra</a>. They're also on-topic on Movies and TV Stack Exchange, with one question each. We won't be leaving anyone out in the cold by refusing these questions.</p>

<p>I think we should encourage anyone who asks a question on these two series here to move their question to Sci-Fi and Fantasy. Although there is definitely crossover in expertise, the majority of Stack Exchange users who are interested in these shows seem to have settled on Sci Fi and Fantasy as their chosen site. As Esq points out in a comment <a href="https://anime.stackexchange.com/questions/24013/is-avatar-korra-bisexual#comment34644_24013">here</a>, it's more important to congregate all the questions in one place than it is to argue philosophy:</p>

<blockquote>
  <p>Anyways whatever the choice is I think avatar should not be split up
  into 2 places, all current Q&amp;A should be moved to a single place.
  Consistency is more important than being right in this case</p>
</blockquote>

<p>Having all the questions in one place means it's easier to find out if your question has already been asked, and it's easier for answerers to find your question since they don't have to check three different sites. Whether or not you think Avatar is anime, the fact is that most of the questions on the show are on SFF.SE, while most of the questions on Full Metal Alchemist and Dragon Ball Z (which are also on-topic on both sites) are over here.</p>

<p>I'm not sure I favor closing any questions on Last Airbender or Korra. I think if we had never decided to take them, it would have been viable to close them as they come in. But at this point, we've already had a policy of allowing them for a while. And it's probably confusing for people to figure out whether they're allowed or not. I'd rather strongly encourage people to move their questions to SFF, with migration as a possibility. Perhaps we could also migrate all currently open questions on these topics, and make it clear in our tag wiki that the tags should not be used for new questions.</p>
 1530: <p>Personally I think they should be allowed.</p>

<p>These are as tangentally related to our userbase as other non-strictly-anime items that we allow are - like manwha. Clearly the userbase is interested in Avatar questions based on how many votes it got.</p>

<p>As for overlapping content, we have many questions about the plots of games - and there's an entire stack site for that.</p>

<p>I think it is fair enough that questions on works that are commonly associated with anime (even though they may not be) are of value to the community because of this status.</p>

<p>Whilst we shouldn't explicitly <em>encourage</em> these questions, I don't think that they shouldn't belong here.</p>
