You can go further than making all restrooms gender neutral.. they can be family bathrooms.
And then you can get rid of gender markers on drving licences, passports, SSN and anything else that has gender identification registered. Unless it is of strict importance (Which I cannot see any reason why it would need to be recorded) should gender be assigned to you.. heck, even birth certificates should say 'a human was born on this day'.. their name and parents.. that is it.. why do we need any gender designation on any legal documentation?