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.