Buck does complicate matters, it's true. But doesn't provide an insurmountable hurdle.
In the absence of third spaces we basically have the choice between accepting the theoretical presence of either a) transmen or b) transwomen in women's spaces. Some women get hurt either way.
It ultimately boils down to: would you rather get undressed next to Buck or next to, eg, Muscato.
Personally I would rather the trans lobby hadn't pushed us to this point in the first place, but we seem to be here now, so I'm going to go for Buck, on the grounds of that one wasn't male-socialised and has a far lower statistical likelihood of assaulting me or getting off on the whole experience.
My push isn't for single sex spaces per se. It's for the protection and maintenance of female spaces. We can have female loos and showers plus open loos and showers, and then everyone's accommodated. Or we can have female loos and male loos and open loos, and everyone's accommodated. Or we can subdivide men over and over into groups rated by likelihood of violence etc, and still have female-only loos and open loos. The point is, there has to be a female-only option.
So Buck can use the men's facilities because these are in fact the open facilities; or we can work together to provide a third, open facility to the benefit of many groups of people if Buck has to be barred from the gents'. There are plenty of ways to accommodate the needs of both women (female) and passing transmen (also female), without opening to door to transwomen (male regardless of passing).
The female class is the protected class. And transgirls, no matter how much they fervently wish otherwise, are not female. They by definition cannot be included in female-only spaces; spaces in which they are permitted are by definition mixed-sex. Which is why they need a mixed-sex facility available. And if we have to turn one of the existing two facilities into a mixed-sex facility, then fine - so long as we keep the other female-only.