Why do people say they hate drama? On social sites sometimes people will state, "I hate drama!", as if to say "if you cause drama, please go away."

My theory is the people who say this, in fact, actually like drama... as evidenced by the apparent hatred for it.  Has there been any research into this?

People could also say, "I hate being kicked in the rear!", which I'm sure most people would hate, and if it happened commonly enough, people may start posting such on their profiles.  This line of thinking leads me to believe that the statement of hatred for drama is the admission that drama is a commonly occurring problem.

Also, it seems to be as reasonable to state this on a profile as it is to hang a sign on a door reading, "I hate thieves!" or a sign on a backside saying, "I hate muggers!"  Since people don't commonly hang these types of signs, why do they hang the drama sign on their profiles?
People certainly express a dislike for drama for different reasons, and I'm going to hazard explaining a few of them that I think are potentially useful:


Expressing an opinion on 'drama', especially on social media, is
usually a response to a critical incident. Just as one
generally does not go around complaining about dishonest auto
mechanics (or car salesmen, or insurance salesmen, or crazy
psychologists...) just to make conversation, one hopefully does not
go around complaining about 'drama' unless one is responding to an
event or set of events in-particular. 

What's different about interpersonal conflict is that, unless one is
a shut-in, there are limitless opportunities to experience it, and
thus there's always a potential cue handy if one wishes to opine.
And oh, how some people love to opine!

This critical incident hypothesis, if you will, is most likely to
explain things like updating a profile or making a particular
comment, etc. It isn't a sufficient explanation for a pattern of
behavior, however - if it seems to be their favorite topic of
discussion, it's probably not a simple critical incident.
If it's a person's favorite complaint, or perhaps with a
dating-style site if it appears as a litmus test or chief complaint,
it could be due to an on-going or past trauma. In other words,
someone has experienced interpersonal conflict they find so
unreasonable, and so deeply hurtful, that it's their most obvious
non-negotiable list item when they go to think about what they don't
want.
The reason the op eludes to is, in my favorite way to explain it, the louder he talked of his honor the faster we counted the spoons. This is something we may refer to as an evaluation
heuristic: when people proclaim how much they are X, the most likely
they are not-X; or the louder they state they hate Y, the more
likely they are to exhibit the traits of Y.

In general, this can be an invaluably useful heuristic. As a woman
if you encounter a man who often favors expressing how much he hates
wife-beaters, for instance, you would likely do best to stay the
hell away from him (as personal anecdote, one of the most vile human
beings I've ever met often expressed his violent disgust for
domestic violence); child-molesters are often witnessed as offering,
unprompted, opinions about treating children well, etc. These sorts
of things are red flags.

And what is a red flag, really? It's something out of the ordinary,
not generally experienced, that we perceive as being "statistically
correlated" with the experience of something bad. Sometimes these
gut feelings are good, sometimes they are mistaken, and they can
often be easily manipulated one way or the other - but one is
generally wise to never simply ignore such intuitions.

Now, to be clear, this is only a heuristic - by definition it can be
wrong, and it doesn't really 'explain' the behavior itself. It's
just a good aid in decision-making.

So while this is often true and valid, I do not offer this as a real
explanation for the behavior. For that I simply continue to...
Selective attentiveness. If a person is dishonest, they surely
know the value of honesty - it gives people the benefit of doubts,
and "confidence" is the resource they most require to be successful
in their manipulations. As such, they are very much aware of honesty
and dishonesty, and actively try to cultivate such opinions. If
someone seems over-eager to gain your trust, there aren't many ways
for that to end well - maybe trying to get you to buy a $20 bottle
of fruit juice, at best.

However, as a criteria this one doesn't have total discriminatory
power - people commonly victimized (the ill and disabled, for
instance, people of low socio-economic class, etc), with PTSD, and
certain personalities might be more focused on honesty and
dishonesty. This is also made harder by context - if there is fear
of being disbelieved or a lack of personal confidence in the self,
this can be thrown way off and a person can be seen as dishonest
falsely. Sadly, this same effect causes con-men to be believed
because they learn to extort this heuristic and direct attention
where they want it.
It's code for something else. What does "drama" even mean? As you
point out, who the heck expresses a preference for interpersonal
conflict and irrational attention seeking?

To them, it may have a specific meaning in their mind: a certain set
of related behaviors, probably mimicking soap-opera like "blow
simple, common experiences out of proportion".

Sometimes, I totally agree - it's important to have perspective, and
if people always have a rain cloud over their head it can be
fatiguing to be around them. However, all too often I've found this
to be a flag for people who express no particular concern, empathy,
or understanding of other people - they just don't care and don't
want to be bothered with "other people's problems". 

This all too often reflects a character of selfishness and unconcern
with others feelings, emotions, and experiences; someone might be
reaching out for a little understanding, or a kind word, or asking
for help, or even suffering from a severe mental or physical
illness, or just venting. Casually dismissing such things as "drama"
is...well, a red flag for me. But again, that's just a heuristic
I've found to be useful.
Critical mass, or "everyone else says it". I'm fun-loving, too!
From a user-experience view (wearing a different hat), requiring
that someone say 'something' without guidance or proper
understanding of what someone should or should not say tends to get
people to just put what they think is appropriate based upon what
other people say or what you tell them they should put.

Depending on where you are, you can find a whole lot of people
saying "no drama". I don't know if they even know what it means, any
more than they know whether or not they are fun-loving or positive
or outgoing or upbeat.
Boorishness. Some people just don't make good conversation, and
maybe they just like to tilt at windmills.
They are middle-school or high-school aged girls. As a father of
two of said human beings, it appears to be in the genetic or
cultural makeup or realities of modern society that generate actual,
imagined, or commentary on, drama.


TLDR;

They might just be, or are in close-contact with, high-school girls. For deeper thinking, see above.