So a porn website (by far, the most effective mean to objectify women) is protesting a law that adds a new layer of social pressure towards women and girls. I don't see men having a problem with women entering mens room. But I do see women feeling uncomfortable with a man entering woman's room. No matter how far will the theory of subjective gender go, it will take decades, if ever, until women and men will simply ig…
I don't understand the type of restrooms you use. When I use the restroom I do not inspect the genitalia of my fellow men. I'm pretty sure women don't do that either. If this is happening in the restroom you utilize you need to find other restrooms.
Under your rules someone who looks, acts, and dresses like a man will be forced (by law!) to use the women's restroom. This actually causes all of the problems you mention. I do not understand your reasoning.