If one views MP’s comedy of men playing women’s parts as part of traditional theater in England (historically men played all parts, including women’s roles, especially in Shakespearian times) then the act of cross-dressing is not punching down, it is a tradition that the anachronism makes humorous.

They certainly mocked gender stereotypes of the era, but even when they had characters that were gay they didn’t really attack the “gay” part, just exaggerated the character’s flamboyance for effect. Another stereotype that we still see in movies and TV today, it hasn’t stopped being humorous, we just acknowledge the stereotype vs any overriding prejudice that may have been more the norm 40-50 years ago.

I’m a pretty big fan, collected all the Flying Circus and movies, and I absolutely could be wrong about my take, it’s been a while since I watched a lot of their act. But I do remember not cringing hard at any of the gender or gay roles. For the time they were pretty kind and didn’t usually directly mock the person for being female or gay, it was just who they were in that role. Nonetheless, some of it wouldn’t work today.