Someone who really thinks he is transgender–to answer your first question. Not every transgender man goes so far as to mutilate his genitals, either. A man who pretends to be transgender just to gain access to a woman’s restroom generally does so just so he can ogle women, get some perverse delight in being where he shouldn’t be, or wants to attack woman and girls when they are most vulnerable.
Because we cannot know if any man dressed as a woman is safe in a restroom, no man, no matter how he is dressed should be allowed in a woman’s restroom. I thought I made that quite clear, but I restate it here more forcefully.