Let's get this party started with a slide from Burning Man's "census" data for 2014. I put census in quotes because, as they readily admit, it's a survey whose results are extrapolated to the whole population, rather than a true census where every single participant is individually counted. It's probably not perfectly accurate, but I think it's likely good enough in terms of broad strokes to serve as a factual basis for discussion. (I'll note that I'm going to try to sidestep the fact that latino/hispanic people can be of any race when it comes to the US census, and consider only non-white latino/hispanics for the purpose of latino/hispanic.)
So, as expected, what we see is non-latino white people over-represented compared to the US population's demographics (84% of 2014 Burning Man attendees were US residents) and even more so compared to the global population. Non-white hispanics (about 18% of the US population) are heavily under-represented and blacks (~12.8% of the US population) are yet more underrepresented.
One interesting thing I find perpetually missing from this 'debate' about racial diversity at Burning Man is people of Asian descent. They are unquestionably a minority in the US (~4.5% of the population) but the discussion around Burning Man never seems to mention them or credit the fact that there are a fair number of Asian minorities at Burning Man. In fact, according to this census, they are slightly over-represented vs. the US population. If you're looking to attack Burning Man because all minorities aren't equally represented, at least acknowledge that just as there are minority groups who don't attend Burning Man very heavily, there are others who do.
In any case, I'm firmly on the 'side' that says that the lack of representation certain minority groups have at Burning Man is not an indictment of the event.
There are probably a number of reasons for some minority groups not coming to BM, including in no particular order:
Cost. Blacks and latinos are less well-off as a whole than white and asian people in the US. Taking off and getting to the BRC to spend a week there is a luxury that only people with lots of money and/or free time (it's possible to go to Burning Man very cheaply if you volunteer and get a free ticket) can indulge in. For most people, going to Burning Man ends up being very expensive. I don't see any reason to be concerned about this vis a vis race though, unless we're also going to fret that poorer people can't take trips to Bali or Paris as easily either. I mean, yes, income inequality is fret-worthy but I don't think there's anything about Burning Man that is any different from the rest of the world in that sense.
Camping. Pick 10 camp grounds at random in the US. Go visit them and tell me what races you mostly see camping there and which you don't. Larry Harvey may have said it awkwardly, but there's nothing wrong with the idea that certain cultures like certain activities more than others.
Group identity. Like it or not, there is a lot of racial clumping in terms of social groups in this country. A lot of white people hang out mainly with white people, a lot of black people hang out mainly with black people, a lot of latinos hang out mainly with other latinos and speak mainly spanish in their communities, etc. I'm not making any justifications or excuses for doing that, nor am I even expressing an opinion about whether it's a good thing or not. But it is a thing, and if you're, say, a black person who prefers the company of other black people, I get how you might look at the sea of often-privileged white people at Burning Man and think, "Not for me." Maybe at a certain point there'll be a critical mass and suddenly someone who previously didn't think it was for them might look at videos of the event and decide that there are enough people like them that they'll feel comfortable there.
Cultural origins. The founders of Burning Man were all white. The original attendees of Burning Man were pretty much all white. If Burning Man had been founded by a group of black people and was primarily black people for the first few years, I suspect the racial composition of Burning Man would look a lot different today than it does. Origins matter, particularly in light of the aforementioned racial clumping in social groups.
That's it. Nothing earthshattering in this post, because I don't think there's much to talk about. I don't think it's any surprise that different events and activities tend to appeal, for a variety of reasons, to different races (especially where culture and race are somewhat tightly tied together like with many minority groups in America). Is skiing somehow racist because it's mostly white?
What is a shame is anyone believing that any race is going to be less than welcome at Burning Man. Racism is alive and well in America, but either people who are less racist than most go to Burning Man (I want to say that's likely, but that would be effectively patting myself on the back, so is a notion to be treated with suspicion) or the culture of the place just encourages people not to express it. Maybe both.
I think it's the friendliest place on Earth, and while I'm a white man and so have no direct experience with what minorities deal with in America or on the playa, I just don't see the kind of attitudes I see off-the-playa towards different racial groups displayed out there. If nothing else, Burning Man is the type of place to make the closed-minded really uncomfortable, so they likely tend to stay away.
I'm sure other people have different perspectives informed by their experiences on the playa. Would love to hear them in the comments!