The trans men question is a complicated one, and the trans argument has demanded a one-size-fits-all approach.
Transwomen retain the same physical advantage over women and commit the same rate of violent and sexual crimes towards women as other men do. Therefore, permitting transwomen to share spaces that are single sex for the reasons of privacy, dignity and safety of women makes no sense at all.
Transmen who take testosterone actually also exhibit a similar strength advantage over other women as men do, but I have not seen any data to show that they commit the same level of crimes as men or women. So therefore it might the case that a transman might be less likely to attack a woman, but the woman might not be able to defend herself if that happened.
In addition, it is harder for women to tell that a transitioned transman is female, which would also lead to discomfort and distress for women in the single sex space and may put the trans man at risk of violence from men. It also means that a transwoman would just start saying that they are a transman and so the issue can still continue. Transmen also do not pose any additional risk to men in their single sex spaces- unless you count the creepy way some of them act towards gay men.
So therefore I suggest that actually it is better for transmen to use male facitlies for the comfort of women, and the fact they pose a reduced risk to men. Hosptial wards would accommodate this by using a private room if available, but women should know that anyone on a single sex womens ward is female.