I'm surprised at some of the responses on this thread, on other similar threads, people have said if they saw a man in their toilets, they would immediately panic, and wouldn't instantly know if it was a trans man or not. Yet here, people are saying they would know instantly.
This "transman" thing is a big red herring. When a man walks into the women's toilets, he is clearly recognizable by his height and body shape as male, and what the women in there wonder is not whether he's a transman, they wonder whether he identifies as woman and they'll be called transphobic for telling him to get the hell out of there.
Transmen who pass as male wouldn't ruin their passing by using the women's toilets, either. An androgynous looking woman can pass as male exactly as long as men do not think to question her sex. If the bearded, short, broad-hipped person comes out of the women's loo, that'll get the men in the bar thinking. Transmen who pass don't want that.
The answers on other threads may well be different because women are not a hivemind.
I, personally, do not really look at people. The way I recognize transwomen who make an effort to look feminine as male is mainly by their height.
If I see a person of normal female height in the women's loo, I don't pay enough attention to notice anything else, I will just assume they're a woman.