Ok, so "mentally challenged," last time I checked, was not on my list of PC terms. And I'm currently taking a class on PC language (among other things).
Unless this particular cheer squad has other issues, his race is irrelevant.
The gay thing is also, mostly irrelevant. Sure, some drag queens are straight up gay, but those mostly aren't actually trying to be "just one of the girls," but are trying to stand out, to "out-girl" the girls. If that is what he is trying to do, then he needs to suck it up. Cheer squad =/= drag show. Uniformity and the team are more important than his art. But again, not really a function of his sexual orientation, and it doesn't sound like the school's objections have anything to do with his sexual orientation.
About the only issue here is that he is male. Ok, but there is room for guys on the cheer squad, right?
But he doesn't want to be a guy on the cheer squad. He wants to be a girl on the cheer squad.
Alright, I guess if he wants to adopt to female gender identity, that might be cool--although as an alternately-gendered individual, he (or she) has fewer legal protections. I'm not sure if any would apply here. I doubt it. Sounds though like he doesn't want to adopt a female gender identity and be one of the girls. Sounds like he wants to pick and choose.
My guess is he wants cheer squad to be his own drag show. Nope, sorry. I'm unsympathetic. I want lots of things to be the Sara Show, but somehow the world is not all that interested in watching the Sara Show. If he wants to put on a drag show, he needs to develop some skills, promote himself, find a venue, and go for it. Cheer squad is not the place.
But then I have seen a cheer squad perform and as someone who has virtually no experience with the concept, I find it pretty repugnant, so my two cents ain't worth much on this issue. And of course, I don't really know what the guy's motives are, the foregoing is mostly an exercise in attempting to combine concepts of inclusiveness with y'know, common sense and logic instead of knee-jerk approval of anything out of the ordinary.