It doesn't matter how they identify and it doesn't matter how they feel. Sometimes you can't have everything you want, just because it's your preference.
Invading another person's space because you want it, even when that person tells you that it makes them uncomfortable is the absolute height of self-entitlement.
And this is the crux of the issue - men are used to getting what they want. It's a patriarchal society. We have single sex spaces set up because we recognise that the female body is more vulnerable and because unfortunately, some men tend to be a bit rapey. But men aren't good at hearing the word "no".
What's happened is that sex and gender have become conflated. It's the biological sex of the individual that matters when assessing risk. A male-bodied individual - statistically - is more likely to commit sexual assault. And that statistical probability actually increases when that male-bodied person has a trans identity.
Not all trans identifying men are sexual deviants. But some are. And inconveniently, they don't wear signs. Plus, it's not just a matter of safety. Women who have previously been subject to male violence or sexual assault don't feel comfortable sharing their single sex spaces with male-bodied individuals. Women of certain religions can't share changing rooms or toilets with male-bodied individuals.
By advocating for male-bodied individuals to use women's single sex spaces, you are prioritising the preferences of men over the safety, well-being, and comfort of women. Do women's feelings and safety not count for anything?!
Also, trans individuals are not a highly vulnerable group. They may feel awkward using men's facilities but there are virtually no instances of assault. Unlike women who are regularly attacked by men, including those with trans identities.
I sympathise with trans identifying men actually, although it might not sound like it. I can imagine it's difficult - but that doesn't mean they have to get their own way. And many refuse to use a third space even when it's available - they INSIST on using women's facilities, which is a huge red flag.
I've already explained that gender critical women aren't the ones who believe in regressive stereotypes. We don't have a problem with "masculine looking women" because "woman" isn't a style.
Male bodies need to be told they have to stay out of women's spaces - and that would make everyone a lot more relaxed than they are right now. In the vast majority of cases, it's fairly obvious which individuals are male - less so in photos, but in person, there are clues that tend to give them away.
I don't think we need checks and clearly that would be really difficult to enforce. But what I think we do need is a very loud and clear message from government that single sex spaces correlate to biological sex, and that gender identity is irrelevant. Currently women have to ensure naked male bodies in their spaces - spas, changing rooms, toilets - we don't need to do an inspection. These individuals seem very happy to strut around with their bodies on clear display - which very much suggests a fetish basis. Women are not a shield from male violence and our spaces are not up for grabs.
I'm sure trans women do feel safer in our spaces, but the point is that many women aren't safer when we have to share them with male bodies, and actually our safety matters too,