Cool, support whatever you like. Unfortunately for you, the standard is still segregated bathrooms.
How about change rooms then? Should heshes be allowed to dangle their weiners in the woman's locker room at say, a public pool?
It would feel a bit strange at first, but personally I think it would have more advantages than disadvantages.
Also, according to your former comment you think also us transguys should use women's locker rooms. It depends on the person, but transguys may also look more like males down there after using hormones for a while (and after bottom-surgery anyway). Wouldn't it be more confusing to meet a transguy in a women's locker room, than meeting people of any gender in a common locker room?
Well, from my own experiences:
I have had to use a common locker room for one of the fitness courses I participated in when I went to university (which I finished a while before I started trying to pass as male), and the males (which were much more common since most courses in the building were for body building) seemed a bit confused by my presence as some asked me if it would be an issue for me to use the same locker room as them. Many had no clue that there was only one locker room in the building and didn't seem to have a huge problem with it when I told them about that, only a bit of confusion.
Might be that females would react a bit more furious if they were the common users of the building and a male stepped in, though.
But that's when people don't expect the locker room to be a common one.
If they expect it, it would become normal. On most fitness courses I went to, many of the long-time members changed clothes in the sports hall and didn't even bother with the locker rooms.
And for completely stripping there are single-person locker rooms at those swimming pools I went to anyway.