Toilets seem, in this discussion, to have become a flashpoint.
I think that is because they are quite a clear illustration of some of the issues. The smallest rooms as a microcosm of the debate over single sex spaces.
So, we have venues that have toilet facilities. Two rooms, one with a picture of a stick figure wearing a skirt. One with a picture of a stick figure wearing trousers.
Society reduces 'gender' to this image, oversimplified to the point of absurdity. Men can wear skirts, women can wear trousers. It's a good illustration of how basic 'gender' and stereotypes are. A form of cultural shorthand. Whole university departments are set up to argue about the mapping of gender onto sex, the effects of this, the potential damage, how to address inequities, whether it's a skirt or a cape, etc.
What the signs signify, though, and what is inside each of those respective rooms, is less lofty and intellectual. It becomes rather basic about human mammalian plumbing. Yes, biologically based.
Males, with penises, can pee standing up. They have the option of using urinals, troughs, or toilets. They can pee anywhere! Lucky them! 'we just want to pee'. Fair enough.
They have no need for sanitary bins for disposal of bloody sanitary towels, tampons, etc. They are never going to deal with flooding, leaks, blood on hands, clothing or legs. They are also never going to have the traumatic experience of miscarrying in a toilet. Males are also less likely to suffer incontinence, higher in females due to women's different biological characteristics and life experiences.
Women can only really use a toilet. These take up more space and use more water. They need access to secure sanitary bins and the ability to wash their hands in private. Most women prefer to be in a single sex space for toileting for this reason.
Women are overwhelmingly the primary care givers with responsibility for small children, so need extra space and provision for this. Due to cultural prejudices, many breastfeeding mothers choose to feed their infants in toilets.
There is also the very clear safety issue.
Women have traditionally used female toilets as a place of escape - where males are culturally prohibited from entering. This is because females are at more risk from males due to males' statistically being more violent, larger and stronger than females. Women are at risk from male violence, including sexual assault.
This is not a cultural interpretation or academic theory. This is all basic fact, evidenced overwhelmingly clearly by statistics.
It's also backed up by millenia of evolved instincts, but that's another subject. Suffice to say females are better at identifying sex than males for very good reasons.
Women were not 'granted' public conveniences until relatively recently. This is the 'urinary leash' - it wasn't considered necessary to allow women to participate in public life to the extent they should have provision of facilities. Women fought hard for public toilets for their dignity, privacy and ability to participate in society.
Women need more space, more provision, more facilities, for all the reasons listed above.
Yet in so many cases, it is the women's toilets that accumulate all the other 'genders' and are signed for 'all genders' or pressured to include males who identify as women, and/or non-binary people.
For the above very clear reasons, women need toilets that exclude all males. For 'toilets' read 'single sex spaces'.
Women exist. It doesn't matter what you do to language, or theory, or the signs on the toilet doors. We still piss out of our urethras, bleed out of our vaginas, birth babies out of our bodies, and face all the messy, sometimes inconvenient issues relating to our sexed biology. Gender is the blue blood on the sanitary towel advert. Sex is the bodily fluid you need to actually deal with in real life.
I know it sounds a little distasteful, and it's nicer to talk about 'gender' as some kind of malleable, fluid, imaginary dream with optional variations and special flags.
But women will still always have female bodies, with all that entails. Sex matters.