I've got nothing against the idea of a third space. It's a nice compromise. But it's impractical to implement. So for that reason, it's only ostensibly going to resolve things.
We managed to implement disabled toilets, after a lot of campaigning. I see no reason that some toilets cannot be designated mixed sex for those who want them.
Trans wings in prison are already a thing. But it would appear, they are not being used much.
I really don't think there are many people who would agree with Karen White in a female prison, I have to say.
But that is where the reluctance to acknowledge the transwomen are men, will lead us.
When you're determined to find no difference, it's hard to step back once you realise the implications.