What I find extraordinary about this is that it's a debate at all.
Every survey properly conducted says most women do not want natal males in their spaces. So women's clearly expressed preferences on fundamental aspects of our own lives are being wholly ignored. Because that suits a small group of male people. How is that acceptable? How is that anything but utterly misogynist?
The fact that some men are dangerous to other males who transgress gender norms is dreadful, and should be vigorously policed and punished. If third spaces are necessary to ensure that transwomen and transmen (because if a transwoman isn't safe in male provision, a transman sure as shit won't be) then those spaces should be provided. They'd help nonbinary people, transmen who feel unsafe in the men's and dysphoric in the women's, and fathers of daughters, too (urinals not ideal when taking a five year old for a pee). It would help any vulnerable individual. If the law mandates that all spaces above a certain size must create new Changing Places equipped disabled loos, with radar key locks, then existing disabled provision could be converted to unisex (while still remaining suitable for many disabled people, thus at a stroke doubling accessible provision). This would meet everyone's needs. Yet it's unpopular with some - some - transwomen. Because it does not meet their wish to have women's bodies around them in a single sex context, to validate their belief that they are one of us. This is a demand to use us, at our own risk and detriment, without reasonable justification and not just without, but actively contra, our consent. It's beyond me, how anyone can argue that that is acceptable. There is no justification in refusing third spaces because you want women as props. It's male patterned entitlement, pure and simple. The demand is that women should show what proportionate means of achieving a legitimate aim can be shown. How about flipping that: what proportionate means of achieving a legitimate aim can transwomen show here? What is the aim, and why is this means proportionate? Sufficiently to harm women in this very clear way?
The single best argument for the fact that almost everyone believes gender is binary is the insistence of those transwomen that we must either have unisex provision, or single sex with their then accessing the women's. If there were any sincere belief that gender is a spectrum, third spaces would be embraced as inherently validating that belief. Instead, they are seen as an insult. Even though it could meet the needs of a range of groups better (and in some cases is the only way that can at all) than any other solution.
Males don't belong in female spaces. Once you start breaking down that simple social contract, women lose the very provision that has enabled us to engage more safely and fully in the world. That should be a key and primary goal for anyone claiming an interest in human rights, because women are the most marginalised group in the world, despite being the largest. We commit vanishingly little crime compared to males, and the single biggest contributor to our safety and dignity and peace of mind is, accordingly, male-free spaces.
Rape, sexual assault, harassment and voyeurism are sadly incredibly common. Of course a large majority of men don't ever perpetrate such crimes, but those who do tend to have many victims. Women have a right to prevent as much risk as we can. It's so blindingly obvious that the best way to do so is to provide spaces segregated by sex, for all women who want that. Which is most of us. Why anyone thinks forcing a change that will harm so many women, to serve the wants of a small group of biological males, when a really obvious, universally respectful solution is there instead, is beyond me.
The stats show transwomen are less likely to be killed or harmed than females. They are clearly not more vulnerable. They have male physical advantage, too. So it's prioritising one group's feelings over another group's safety and feelings, and the sole identifiable reason for this is that the group whose needs are being prioritised are male. And as a society, we are conditioned to reflex level to always, always think about male wants and needs ahead of women's. To the point that a woman not doing so is seen as an oppressor.