Therefore we are not discriminating against men, either directly or indirectly, if all they have to do is say "I identify as a woman" and they will be allowed in.
At which point, by the time you've made that clear, what's the point of making this so confusing and trying to basically cause collisions with discrimination legislation? Why don't you just ask everyone "do you want to come in?"
I still think you're in potential trouble here - you could say you've got a group for people who say they don't identify as Jewish. And you could claim that's not a problem, because anyone who is Jewish can come in - all they have to do is say "I don't identify as Jewish".
But forcing a particular protected group to lie to gain entry, while not requiring others to lie, is another form of discrimination.
You'd have to try to claim that "identify as" is meaningless, as is the word "Jewish" in this context, thus you're not asking anyone to make any sort of meaningful statement about themselves - it's just a meaningless phrase.
Every single attempt to push "gender" is going to have to rely on making it and the concept of "identity" more and more meaningless, and less and less connected to sex.