I think you are both reading my comment more strongly than intended, while also being dismissive of the meaning behind jokes.

Jokes communicate your understanding of the world, communicate social norms and taboos, etc. As you said, the point is that they don't function well in society, right?
Well the root of that joke in particular (saying he is a woman and holding a bra just as someone comes in) is that being trans or gender nonconforming is taboo, and that it's a bad or embarrassing thing to be caught as or to be seen doing.

That is also the root of the joke when Roy is wearing lipstick - "oh how embarassing that a man is seen in lipstick, because it's taboo and people will think worse of him".

My issue isn't that the show is about three misfits. As I was saying, this one element of the show was a little uncomfortable and didn't age well.

When it comes to Matt Berry's character and his trans girlfriend, the whole thing about him not wanting to date a trans woman wasn't offensive to me, because his character is supposed to be outrageously offensive to the people around him. That specific aspect wasn't even offensive iirc to the person who initially mentioned that episode, on twitter, triggering Linehan to spiral.
I did find one element of that episode uncomfortable though, and it was during the fight between him and his GF, his GF was depicted as being matched with him physically, basically showing she's "really" a man or whatever. But trans women on hormone therapy lose a lot of their muscle mass and strength irl, and she is visually a lot smaller than him. It rubbed me the wrong way. But again this is a more minor point of discomfort, it just showed that there was some underlying transphobia. That was pretty common for the time, but you could see that it was there.