Is it standard for US-based universities to consider the ethnicity of an applicant during PhD admissions?
If there is one thing that academia is particularly bad at, it is transparency in decision making. Why do some people get admitted and not others? Why are some people hired and not others? Why are some people promoted and not others? From the bottom to the top of academic hierarchy, you'll be hard-pressed to ever get a straight answer, and answers you do get are always suspect because the nature of human decision-making is itself complex and opaque. There are plenty of reasons for this, from self-protection from criticism and gaming of the system, to rapidly changing criteria based on past experience and argument, to the fact that so much of the decision making is based on subjective ratings provided by individuals (often down to individual faculty members deciding if they want to work with a student). 

To cut to the heart of your question, while it is not any sort of prescribed standard at the graduate level, you can safely assume race, ethnicity, national origin, and gender will be in some way be "taken into account" by some committees and individual professors. In many states this is actually illegal, explicitly forbidden by law - you can still assume it will sometimes happen anyway. On the other hand, some people will simply ignore demographic factors to the extent they are physically able, regardless of what they are told to do. As Universities have a history of avoiding transparency in admissions, you are extremely unlikely to ever know when it was considered, how much effect it had, whether it was positive or negative, and whether it ended up materially effecting the decision to admit you or not. You cannot know, they will basically never tell you, they will tend to go out of their way to avoid writing it down, and it is common for many people in the process to not even know with any certainty what factors ultimately "mattered".

However, from what I've seen on the inside and the outside of academia and from talking to fellow academics, you can safely assume at the graduate level that other factors matter way, way more. It is simply too high-stakes a decision for most schools to be altruistic, and they tend to steadfastly refuse to intentionally admit people who are utterly unqualified simply because of some demographic fact about them. The vast majority of Universities will only admit you if they think you will do well there, because having a bunch of under-performing students who are radically unqualified to pursue research and teaching is an albatross around the neck that few graduate schools will willingly tolerate. This is even more true at the PhD level, because they aren't cashing in on tuition (which is heavily marked up for international students, because money), so performance is king. 

From talking to people working on diversity initiatives, I'll also give you another important insight: the diversity initiatives you hear about are not actually a preoccupation of the majority of faculty and staff, for good or ill. According to people working on actually making these initiatives successful, they report that the vast majority of people mostly want to ignore the issue and focus on other things, and so they work so very hard to make the initiatives public and heavily seen because otherwise they feel they will be unable to make any changes and they will be crushed by the majority weight of indifference mixed in with a heavy dose of active hostility to their efforts. Higher ed can look monolithic from the outside - but on the inside it is highly factious, and what appears as consensus is often a thin facade.

Because of all the above, the only advice I think makes any sense is treat the process as any other student should: apply broadly, see what offers you get, and talk with prospective advisors about what they are interested in. You are welcome to ask them if they were involved in your admission decision and then ask them why they wanted to admit you; I did that, and while it can feel a little awkward at first, a little bit of humor makes it easier and most professors when questioned directly, sincerely, and politely gave very direct answers. Some even said what parts of my profile they thought were a concern, and what other parts they thought would be a strength. Everyone gave wildly different answers, there was no consistency - no two people see the same person the same way.

Once you've got all your offers and finished talking with people, you can make your decision then on what seems like the best opportunity for you.