Jelly, the robotics are amazing.
Regarding the theme I fear you may be walking an incredibly thin line when it comes to "laughing with" vs. "laughing at" a group that still faces legally sanctioned discrimination. (marriage, military service, no protections at the federal level, etc...) I have been on a few gay related mailing lists that have brought up your art piece out of concern for the negative direction it could take. So it is with that in mind that I embark on the rest of this reply to your OP.
Clearly you have a flare for eccentric characters, and this one shouldn't be any less eccentric. I suggest that you don't make his sexuality the punchline though. Being effeminate is not necessarily a gay trait, and neither is enjoying musical theater. Look at Liza's most recent husband David Gest (hmmm... David Gest... sure sounds a lot like....) Now that is fodder for an eccentric character. In fact, if you look at some of the most successful send ups of gay men, it has been done in the form of a gay man in denial, or a gay man in the closet. Smithers on the Simpsons comes to mind immediately.
If you insist on making the character an out gay man I suggest you research how writers/directors/actors have telegraphed someone or something as "gay" to a gay audience without clueing in the non-gay audience. I've heard this referred to as "the pink window" gays see the pink glass, the non-gay audience just sees the world on the other side.
On a personal note even in San Francisco I get called a faggot for holding my partners hand no less than once a week. In the Castro (gay) district it is very common for somebody in a car to yell "faggot" out the window while driving down Market. And once or twice a month I read stories in the gay newspaper about a gay man who was attacked or killed here in our safehaven for gayness, because he was gay. Black Rock City is full of people from all over the US (and the world), and not all of them have a welcoming attitude regarding gays. Even in BRC a couple years ago I had friends angrily confronted and told that faggots were not welcome in certain esplanade camps. The reason I'm telling you this is so that you don't make the mistake of thinking that gays feel 100% welcome in BRC, and therefore won't mind a ribbing.
I worry less about the adult gay men though, and more about the young, not-yet-out gay boy exploring the city with his parents. He doesn't even yet fully understand his sexuality, and knows only what he has seen on TV, been told by his classmates, or heard adults talking about. I remember when that was me. I was 17, and in my American Political Systems class in a suburban public school of Los Angeles. The teacher for the class was a right wing nut who brought in The Christian Coalition for Family Value's video entitled "The Homosexual Agenda" to show in class. I sat there in my assigned front row seat as the video droned on about the "disgusting sexual habits of gay men" describing the diseases that infest gays, and how they want to rape children. Goebbels would have been proud. I could feel my classmates absorbing this misinformation as fact. I could hear them groaning in disgust at the graphic explanation of mythical sexual acts like felching and snow balling. It felt like all my classmates were disapproving of me directly (even if they didn't know.) I have never been able to live down that class, and I'm in my 30s now. It still makes my angry. I hope someday some now out gay guy finds that teacher, now retired, and beats the shit out of him for every gay kid that he destroyed like he destroyed me that day.
The point is Jelly, depending on how you do this, it could be great, or it could be devastating. You'll get approval from certain segments of BRC no matter which it is. I'll just hope that greatness is what you achieve.