It won't work.
Because it's not about a safe space to pee, or equal recognition or anything else sensible. It's about forcing the world to acknowledge that their personal choice trumps everything and everyone, reality be damned. It's extreme narcissism. Its being in the room marked Men with biological men for that buzz of 'look at me being and doing what I choose'. It's about smashing the boundary in people's faces. For people with APG there's the additional massive kick of women hopefully being in a state of undress with tampons hanging out all around them, and for some women being scared and uncomfortable makes the thrill all the hotter.
Unless the government has the guts to draw the line on this and say gender is everyone's choice, sex is, sex spaces ARE protected by law and gender neutral spaces must be provided for those choosing not to use the space provided for their sex then 99% of the population becomes the toys of the 1%. Collateral damage.