I know this is three years late but cool, I'm also Jewish! Orthodox to be exact. I'm sorry you had those experiences with those people in shuls, not all of us are like that.
-I'm just going to correct what you said about the sexual parts of a Jewish relationship.-
It is a mitzvah (commandment) for men and men alone to have kids. Obviously, that's sort of impossible without someone's uterus being involved. So when men need to have sex, they must make sure their wives are also enjoying-it shouldn't just be about them.
As for god being agender-yes we believe that. God also has "feminine" and "masculine" qualities, so when God is acting in whichever one, we refer to it as She/Him, depending.
Jewish is an ethnicity. It means nothing on your religious belief. You can be Jewish and pagan, Jewish and be a Christian... It's a legacy and something you can't change; it's your DNA. (/nm, just wanted to say this point and it kind of connected to what you're saying, I'm not attacking you-you actually agree with what I am saying.)
Anywhoooo, the religion would be Judaism, but anyone could **in theory** be Jewish, even if they don't practice that.