Treating someone who seems like a woman, acts like a woman, is at risk from the gender-based violence inflicted upon women… as a man… is making people safer, how exactly?
How would you even determine which women to exclude? If someone's saying "hey, I'm trans, I'll leave if my existence makes you uncomfortable", they're clearly not one of the Evil™ Ones… so are you proposing to check everyone who enters these spaces? Oh, but wait, the state of medical treatment is actually pretty good, these days. Better make that a thorough check. (No. Just, no.)
And how is it a good idea to put trans men in with women victims of (usually male-perpetrated) domestic violence? Isn't the whole point of the "women's spaces" thing to avoid that? (Or do you propose to just ban all trans people from support services entirely?)