Saying you must be part of the "identity group" you are telling a joke about is gatekeeping. That is PC culture in a nutshell.
Why do people like Chappelle need to make fun of a group that is fighting for their rights and recognition across the world?
He's signalling that trans people should not be recognized as themselves, and their issues not taken seriously.
At this point it doesn't matter if people laugh at the end.
That said, suggesting there is a binary power structure is incorrect in the first place.