Dunno if you saw this, which I just posted: https://medium.com/a-universalist-in-an-identitarian-age/the-meaninglessness-of-lived-experience-on-jessica-krug-rachel-dolezal-and-passing-as-black-d259aa3d003a
I think you are offering contradictory examples.
Being French is cultural. You can become French, and you can learn French.
We don’t know whether someone is born gay or becomes gay, but it doesn’t matter: either you are romantically attracted to people of your sex or you are not.
I think your black Jewish friend was looking for purpose, saw Judaism on her birth certificate, and decided that was it. I am unable to believe in predestination or a Jewish gene that would explain things otherwise. Mind you, I wouldn’t tell her that unless it came up—it’s a harmless belief.
You agree that trans people should not be limited by their sex. I trust you’re also aware of the “dead names” taboo. There are trans people who want to focus on what they are now.
Why then should someone be limited by their genetic heritage? Is the argument here that Krug and Dolezal must be bound by something that doesn’t exist?
That said, I agree no one likes to be lied to. But when addressing the issue, you have to ask what’s gained by lying. Did they acquire black privilege?