Another of my posts yesterday emphasised the importance of these concrete questions on the basis that threads like these, while fascinating - looking forward to following this one - can become a bit circuitous, an an explanation of why: it may move such threads forward even further. Just as an eg.
Tandora, above, you write,
[Calling a space for trans women and women 'mixed sex'] is also unreasonable as it completely fails to recognise that "trans women" (whether you believe they are a "subset of men" or not) still exist as a distinct category of people.
I could equally write:
[Calling a space for trans women and women 'single sex'] is also unreasonable as it completely fails to recognise that "women" (whether you believe they are a "subset of the group trans women and women" or not) still exist as a distinct category of people.
In other words, you term 'unreasonable', in this context, just doesn't make sense unless as an indication of a parallel failure to recognise that women, in the way the women here wish to define themselves (female; sex-based), still exist as a 'distinct category of people'.
Other adjectives could be applied: complex, difficult, thought-provoking etc. But 'unreasonable' doesn't hold up.
It's issues like this that lead me to request some more concrete details re: your views.