Their jokes about assigning gender to babies and to being transgender, dressing in drag, like all of it was a send-up.
Sure, they did punch down if you were a person who were in those groups, but the fact that it was large enough social event to be relevant enough to be a comedy skit on a television show or a movie seen by millions implies that there were some serious things going on back then that they could see and wanted to address.
What the hell was going on that put all of those things in their mind?
Well, Graham Chapman was quite openly gay, it’s not surprizing they didn’t mock gays.
uh they frequently did, they had a whole sketch which is just them saying “no pooftahs” (equivalent of the f-slur)
They were making fun of the people saying that in the sketch. The guy saying “no pooftahs” there was Graham Chapman himself :)