If most men are kind (as I believe they are) - there's no problem with feminine boys/men using the mens
I do see a problem here with 'most', especially in schools.
Amongst 500 boys in an average secondary, there are probably 10% or so who are gits, so a male transgirl using the boys' facilities is likely to run into at least one of them daily.
Whereas, if you stick the male transgirl in the girls instead, there's probably a similar 10% chance that that particular transgirl is a git and thus an actual hazard to the girls.
So I can see why schools do it. That still removes the safe feelings and privacy of the girls, though.
I can see why some people campaign for the safety and dignity of the transgirl, but not why they choose to ignore those of the girls.