We generally established that "I don't feel comfortable being around them" is not an excuse to discriminate back in the 60s.
To clarify: would you argue that the existence of separate drinking fountains for white people and black people is justified because many white people feel uncomfortable drinking from the same fountain a black person has just used? If not, why not?
I have to say that I have seen a lot of arguments in support of bathroom bans, but trans women have stinkier shits is new to me and perhaps the most outlandishly petty reason I could imagine. So while I disagree with the entirety of your post, I will give you kudos for coming up with that one.