It could be that those women who so adamantly oppose the idea of any single-sex spaces for women in rape crisis counseling have staked their own beliefs on trans women absolutely being women #nodebate, and if that is the case, then they will reject any call for single-sex female spaces.
I see your point, but no, I can't see that they truly believe TWAW.
They are not treating TW as they treat women; they have two very different standards of treatment and viewed entitlement and it is wholly sexed based . Quite how much they are lying to themselves to be able to rationalise in their heads, I don't know. There's a whole lot of status and self congratulation and lovely mummy/noble saviour feelings that become obvious quite quickly in many discussions. (#codependence)
It is nothing more exciting than a fixed belief that males must be served by females, and females must be subordinated. It's millenia old misogyny and sexism. And it's unacceptable.
Male people's diverse needs can and should be met, and not ever by sacrificing females to gratify or placate them. Aesop's fable of dog in the manger is highly appropriate reading.