Nazis were obsessed with maintaining the 'purity' of a sex class defined by a biological essentialist view of them as womb bearers who had to be protected at all costs, and much of their propaganda revolved around the idea of the monstrous, degenerate Other invading and defiling this fragile, precious and sacred breeding resource.
That doesn't mean the sex class didn't exist. How did the Nazis know which people to oppress in this way? Are you saying that if you walked into a room while the Nazis were coming, you wouldn't know which people to try to save from that fate? That instead you'd start telling the Nazis these people didn't exist, or that you'd become one of them if you wore a skirt, and that would somehow bamboozle them into leaving them alone out of confusion?
The oppression is precisely because women exist as a sex class, and when oppression is sex based, protections must be sex based too. Schindler and Hitler both knew what a Jew was, doesn't mean they were the same as each other.
As for the rest of it, with all the violence against people who dissented from the authoritarianism, I can't believe you don't see that mirrored in all the threats to rape, hang, stab, shoot and immolate people who refuse to say men are women. And did you notice these guys also seem to always know at which class of people to direct these threats?