How would this work in your example? What could prevent me from saying I'm gender fluid and walk into the women's showers at the gym?
If we're ready to take the step to say that there is no gender binary then we kind of have to go the whole way and flip to communal showers/bathrooms/dressing rooms etc. Reading your comment reminds me of the obscenity law debates in 1964 when Justice Potter Stewart said...
"I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description ["hard-core pornography"], and perhaps I could never succeed in intelligibly doing so. But I know it when I see it,"
If we aren't ready to make the big leap to no recognized genders (which I would argue society at large is not ready for), then standards need to exist from a legal point of view in the mean time.
A person's perceived gender (which will be a function of that's person's subjective gender identity, among other things) will play a major role in determining whether a person's conduct is perceived in this way. A woman in a women's bathroom would likely have to do something pretty overt to get herself in trouble. A person who appears to be a man will, presumably, be on much thinner ice. It seems to me that a combination of this and the prevailing social pressure not to wander into the wrong bathroom should be all we need. And, after all, nobody to my knowledge has ever presented a shred of evidence that there is actually a problem with people using the "wrong" bathroom to warrant the sort of legislation we're talking about--especially when that legislation will indisputably harm an already marginalized segment of the population.
How does this law prevent anyone from doing that already?
But given direction these new laws are taking, I'm further guessing that the Police should refuse to remove the man and instead arrest the proprietor for discriminating against this man based on his protected status of identifying as a woman?
As evinced by the fact that unisex bathrooms were the norm until the late 19th-early 20th century, and that rest stops and other establishments operate unisex bathrooms without any issue.
I think the problem (illustrated nicely by your comment) is that, in reality, gender is too complex and varied to be adequately addressed by this sort of legislation. While its easy enough to this sort of law to work properly 95% of the time, its hard to come up with a real legal test that doesn't leave some percentage of people marginalized and legally required to use the wrong bathroom (either because its not the one they would feel comfortable using, or also in many cases because it would make the other users of that bathroom uncomfortable).
This being the case, and given a complete lack of any real problem with bathroom use today, one would think that this counsels strongly in favor of having no specific law on the subject at all, and relying instead on the usual social convention. (Bearing in mind, of course, that in the extremely rare event that someone really does stroll into the wrong bathroom for voyeuristic purposes, or to sexually assault someone, we already have laws to punish those people.)
It never ceases to amaze me that people who are normally so quick to declaim against any purported intrusion into individual liberties (note that I'm not necessarily talking about you here) are happy to uncritically accept the proposition that the government should have a role in telling you which bathroom you can and cannot use.