"You seem to have chosen to categorise people by “biological sex
Yes, for some things this is important, is it not? Where we differentiate by sex? There aren’t that many things, but the one that there are its extremely important. The bogs are important because women are vulnerable to sexual assault from males. So there we segregate by sex. which other criteria would one segregate by? "
.....
Plus,
We have different toilet needs.
Men can piss in or against things standing up. They have a thing called a willy, knob or little-dicky-doo-dah like a tiny multifunction hosepipe thing they can piss out of. For this reason, for speed, comfort, to avoid queues etc many gents toilets are fitted with a trough thing or extra things a bit like basins called "urinals". There are complex man-rules around the use of urinals, about where you can and can't look and eye contact and little games with the disinfectant thingys but I don't know the detail as I'm not a man and I haven't got a little willy and I can't piss standing up.
Moving on to the other manufactured irrelevant to toilets group - women. Women have these things called periods or "exclusionary grossness" that I can't therefore talk about but has consequences from a toileting perspective. Because they are inadequately born without a little dicky-do-dah like normal people, they can't piss standing up, so always need cubicles. And special disposal facilities. That I can't talk about for bringing on a fit of the vapours in any normal strong penis-people who might be reading.
In summary. Having separate toilets for men and women on a sex basis is a pragmatic solution to our different biologcial needs and the fact that a very large minority of men are total pervy freaks and we don't want them anywhere near us thanks.
Tell us more why splitting things out on teh basis of internal feelings of gender is a MORE pragmatic solution. And SEX is totally irrelevant.