I'm going to cheat, and restate the OP as 'who wants nakedness and toileting to be strictly sex-segregated?'
Lots of PP make the point that even if only a minority need it (say, a religious minority), then there must be at least some sex-segregated provision, for them not to be excluded from wider society.
That seems a little unambitious though, given that the answer to OP's question is actually 'everybody'. 100% of people.
Conservatives want it in order to control female fertility, and police paternity.
Liberals want it in order to preserve freedom of movement for more physically vulnerable humans.
Feminists want it insofar as it is one example of the derogations permitted by law from strict sex non-discrimination, with the purpose of mitigating the disadvantages women suffer as a result of their biology.
Transwomen want it so they can be the only people not bound by it.
Everyone else wants it because it's instinctive, and anything else is taboo. For perfectly good evolutionary reasons including ones around reproductive strategies and the need to avoid being eaten by a predator whilst copulating or defecating.
So let's do it!
I'm not a monster though. Mob rule is bad, so if the TW are too frightened to mix with other males, let them have a space of their own. They are not many, so it should be easy to do.