I think protesting that way are weird, but.. ok. People do what they want :X and IMO, bathrooms should be designed per genital because of the equipment instaled inside.
But there's a better solution:
We put a tiny microchip in everyone's skull, which will give the person their gender/urinating apparatus designation. And, on every single bathroom doorframe, we place a little sensor. Anyone must register their final gender/urinating apparatus identification with the gov before they can use a public bathroom for the first time.
-If a person's register doesn't match the doorframe's desired code, the chip will get horribly hot until the person leaves the bathroom. Easy!