To completely sidestep gender identity laws, why not have bathroom facilities based upon dick or no dick?
Have a dick? You must use this room to piss or change.
Do not have a dick? You must use this room to piss or change.
100% just boil it down to cock or no cock. I expect having it based upon anatomical reality of one specific organ can't be construed as denying gender identity. It's just cut and dry anatomy standards.
We already have this with signs for "Men" and "Women". They are the ones who redefined those words to be something else.