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?
I was there when the deep magic was written (or soon after to catch reruns), Monty Python was skewering the Post War Conservative British cultural zeitgeist in ways which audiences hadn’t quite seen before, through the lens of British toffs (oxford and cambridge) playing at being proletarians skewering toffs. It was different for British TV, but it was like a sea change when American audiences finally caught up and began taking notice. It was smart comedy, pointed, brutal, and hilarious. America wasn’t doing anything like this, at that time, going more for the broad jokes that would appeal to the lowest common denominator. Sure others have mentioned Brooks, and Berle, and Cartoons which had been sending up cultural norms for decades, but they weren’t Python, Python, at the time were a thing of their own. Monty Python’s Flying Circus ran from 1969 to 1974. Saturday Night Live started in 1975.