Fourth option. They are a TW doing all the usual mental gymnastics and word salad inventing to suggest that we really can't ever know what a woman is.
Fair enough. So here's your definition.
Men and women are (mostly) the same. They can do the same things (taking care of children, being a dancer, being a CEO, nurse, judge, president, wtv). However there are some physical differences, both genetic, internal and external. Because of these men have tended to sexually, physically and emotionally torture women, for millennia, and murder them as well. Because of this, women tend to be sh*t scared of men, and need sex segregated safe spaces, especially when we're talking about states of undress or unconsciousness/powerlessness (sleeping, hospital wards, refuges......).
Soooo if you are transitioning the question you need to really ask yourself is: are you scary to women?
The women you see in a public bathroom don't know you, so they judge you by appearance alone. 🤷🏻♀️ So, could you potentially be a threat to them? "Could" being an important word here. I'm not saying you are! (I still tell my kids not to run with scissors. That doesn't mean they are 100% going to hurt themselves, but they COULD)