What is comedy's respondsibility to public discourse?? A comedian's first and arguably only job is to make people laugh. Dave's 95% score on Rotten Tomatoes suggests he succeeded.
I think this is the mistake that most of the more strident critics of the show are making. Maybe you'll claim that this is hiding behind comedy, but actually it's about clarifying what comedy is.
If you want to claim that his "oppression Olympics" joke (which we've already agreed was bad) was "shit-stirring" I actuallly wouldn't particularly argue with that. I'd clarify that I think only a tiny, tiny minority of peple will hear that joke and say "yeah, trans people are so privileged compared to black people! Fuck those guys". Especially as we're aware that black trans people exist.
But sure. It was an unfunny joke that made no wider point. I'd expect a comedian of Dave's stature to do better. (Incidentally, it seems your entire criticism of Dave's show is centred around this joke. Is that a fair assessment?)
But what I'm pressing you for is precision. "Shit-stirring"? Yeah, I guess you could say that. Bigotry? No. Obviously not.
Chalking up somebody's "existence" to this narrow binary is not bigoted. It's simplistic. Stupid even. But words have meanings. If I say white people have it easier than black people, I'm chalking white people's "existence" to that narrow binary, and there will be numerous cases where I'm wrong, but I'm not bigoted. I'm just wrong.