I’m not a believer in the ‘rights’ concept at all — not only because it is a philosophical nonsense, but also because those who politically bang on about ‘rights’ are often the first to act at odds with such supposed rights.
Trans people are likely to have problems with whichever bathroom they use. In general, heterosexual people can be ill at ease finding either the opposite sex masquerading as their own sex or their own sex masquerading as the opposite. A guy converting with a ‘lady-tech’ might get a doing over in some gents loos, whereas he can easily creep the hell out of women in the ladies.
This sort of problem seems to be ignored in the rush to ‘respect the rights’ of these people. It’s that old road to hell paved with good intentions. It might be kinder to let these people know that no matter how many champions of their situation show up to support them, the wider world will still tend to see them as oddities. Whether anyone thinks that reality is ‘right’ or ‘wrong’ is irrelevant — it is just the way things are. Denying the challenges confronting anyone with their way of life is worse than useless. ‘Society’ is never going to turn itself upside down for any minority, and those who are forever arguing that it should, only create resentment against the minorities they imagine they are helping.
Just as an aside, there is still the odd place here in France where there are no ‘sexed’ bathrooms. You have a shared wash and mirror area, and a set of effectively unisex stalls/cubicles. It is actually quite a humanizing experience to share a word or two with the opposite sex as you dry your hands, but I am not sure it suits the ladies so well when they want to check their makeup or sort their bra.