To try and answer your question, OP
Most of the time, it really doesn't matter to me personally whether a generic activity - evening class, orchestra, neighbourhood watch meeting - is mixed or single sex, maybe because I think of myself as a person first and foremost - and because I have been fortunate enough throughout my life to have had positive relationships with men.
But I want to know what the rules are at the outset, so I can make an informed choice. A bit like ordering in a restaurant where you decide beforehand if you are going to share with anyone or not. Don't decide once we've ordered that you would like half the food on my plate...
However, for anything where I may be in a vulnerable position, undressed, incapacitated etc it really does matter to me and I then would want to be in a female only space. I don't believe that people can change sex, so a male person, no matter what medication or cosmetic surgery they have done to their body, can never be a female person.
As for the 1950s jibe earlier, I have a lovely family with whom I am fortunate to be entirely safe and yet, for my own privacy and dignity, I don't choose to be undressed in front of them. My personal boundaries.
If I go swimming I ideally like to change in a single lockable cubicle but, failing that, the camaraderie of a single sex space is fine. I have never felt physically threatened on any level by a woman and experience a sense of relief and relaxation when it is an all female environment, though I still manoeuvre a mean towel!
When my boys and girls were very young we used to pop them all in the bath together but as soon as each hit a time when they expressed any discomfort, they showered by themselves. Because we respected their boundaries.
Every day around the world, literally millions of highly vulnerable people use men's single sex facilities, thankfully almost without incident.
They are called...boys.
The idea then that a 6' adult male person (regardless of their clothes or the unlikely but possible neo-arrangement of their genitals) using the male toilets/changing facilities is more vulnerable on any level than a 7 year old boy is, quite frankly, balderdash.
And just because some males have been overriding boundaries and making women feel uncomfortable in their own space for 40+ years, doesn't mean other male people can get to do so with impunity.
We were not asked if this was OK back in 2004 and we did not and do not consent to this.
The males who use female spaces to shore up their belief that they are a woman are not nice people if they are choosing to trample over my boundaries and consent when I have said no.
And I am saying no.