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.
Why not have a sign over a door with a pictured urinal. Say this is the bathroom with urinals and see if anyone complains.