Sex and gender are two different things.
How your body was formed and what it can do is not the same thing as your identity. A father of two can have a female self identity. And they may have been "in the closet" about it for over 50 years because of their fears of rejection in a society that is hostile to transfolks.
So some men, really, really, believe that they are women.
Yeah, we know this.
But they’re not.
I really, really, really believe that I'm a progressive billionaire who is 6 feet tall. I really, truly, believe it.
If I had some way of testing your sincerity, via psychological screening, brain scans, or some other method, and it mattered for some reason, like I was deciding which prison you belong in, then I would be in favor of examining your claims in greater detail.**
But since I don't have psychic powers, testing would cost money, and I don't give a shit what you believe about yourself, then my response is "meh". Think what you like, identify as you wish, live and let live.
You can't get rid of sexism by enshrining it. Yes, there are differences between the sexes, and yes, they can affect important things like health care and careers, so we should be mindful of the differences and mitigate the negative social impacts as much as possible. But very little in our everyday lives needs to be about sex or gender. Most of it can be universal among human beings regardless of how they "present". I don't care which public restroom
Conchita Wurst uses. I care that everyone in the restrooms is being polite and respectful towards each other.