Remember, equality means equal for ALL, so a transgender person is not more important than a boring cis male.
The only downside to a rest room that is non gender, is the moment you leave the stall, you have to have your pants done up properly, you need to have your dress adjusted correctly and you can't walk in wearing outfit A, and get undressed in front of the sink and change into outfit B regardless of what outfit A and B are.
You can adjust your lipstick, you can fix your tie, you can take off a shoe and remove a stone, but the rest of the people in the room expect you to be properly dressed otherwise.
A proper genderless rest room has no urinals, regardless of whether you as a lady can do a decent aim from your gear or not. The guys might not want to see you do it, they might not want you looking while they give their own the allowable maximum shakes after going.
My only concern, is I have seen lots and lots of stalls in my time, and they are hardly what I would call entirely private. You can stand next to many and see over, you can often see plenty under. And once you have made the stall an entirely enclosed room, it's a separate room and the discussion becomes moot.
Ideally, a well designed rest room is that. A common outer room with a sink and a mirror if you desperately need it. And a row of actual separate rooms that are just that entirely separate rooms and fully enclosed with a full on door. At that point, they are not required to be all gender if only one person can use it at a time. If you have 10 rooms, all only open to a single person at a time, it is no different than having a men's room right next to a women's room in the building.
Make a toilet an entirely enclosed room with nothing but a toilet, problem solved. Then it becomes a case of telling people, don't do anything in front of the sink and mirror, you wouldn't do out in the rest of the building.
