@mummyduckduck - I hope this thread has been helpful for you.
Most people coming on to ask the sort of questions you ask - and there are a lot of them - have absolutely no intention of listening and learning, which is why you've had the reception you've had. You've also had some patient souls explain things in a way that hopefully helps you to understand.
I'm a liberal lefty. I've always been completely supportive of LGBT rights, I have close family members and many friends in that community.
A few years ago now, I unquestioningly supported trans rights and trans women's belief that 'transwomen are women' (note: it's rare you hear transmen angrily and vociferously insisting that 'transmen are men').
But Mumsnet opened my eyes. Opened them big time.
I'm like you. Pretty 'sheltered'. I mean, I've lived and travelled in the world. But the men around me are all nice, non-predatory types, I've never been raped or sexually assaulted (countless low level stuff, of course).
I don't need to have any personal issues or concerns, because I'm one of the lucky ones.
But it's not just about me, it is?
Women have women-only spaces because we (as a group) need them. Not very individual (like you, or me) will need all of them, or perhaps even any of them. But most women will need to access at least some of those spaces at some point in time. And they need to be able to make their own decisions about what they consent to.
Likewise, predatory men don't come with a handy sign. Men are also physically stronger than women.
Sport. I've never really played sport. Not my thing. Never really watched it. But even I can see how impotent we women are as a group, standing by, watching male-bodied people (men) infiltrating our competitions and cheating.
Women's rights - 50% of the population - are being seriously eroded for a tiny, vocal, minority.