Please lets remember that since there have been public loos, changing rooms, loos in dept stores, some people have used the ones that do not correspond with their birth sex. Often for most of their lives.
Although we often read that" we can always spot them", it ain't so. Usually, but not always. Males ( and we are talking about males, really) vary hugely in build., and in natural levels of testosterone. Some have little or none of the strong jawbone and prominent ridges above the eyes, and so on, and some are if slight height and build.
When someone who is not of strongly male build has been living " as a woman" for 30 years, and has worked at it , they may well pass under the radar.
So the situation at the moment is as it is. Transsexual women, and indeed trans people, are " in the spaces. " Not often, and very rarely with bad outcomes. The problem remains; what the hell happens if thousands of trans women suddenly invade?
I don't know.But just saying " we are not having it" may not solve the problem. The least worst solution might be to stick with the current system.
According to my mother my daughter, and my sisters, I do not get glanced at in the mirrors in the loos. I've never had " ere' there's a geezer in here" comment when I have been in a cubicle. But tbh I don't pass wonderfully well, if people have a hard look at me. I think people are just getting on with life, and as long as there is no evil intention, tend not to take much notice.
Though when I transitioned, at UCA, I did not use the ladies loos for the first year, because I can't tell who has good reason to be alarmed at males in the ladies. Would I go back to using the gents, after two decades? Sorry, but no.