You're clearly a great mom to your non-binary child, and I'm not in any way saying their identity isn't valid.

You said yourself though "to be what society considers feminine". What America/Western countries consider feminine, what colours, what mannerisms, speech patterns etc are considered feminine are not universal and are certainly not "hard wired in utero". A hundred years ago, pink was a masculine colour. In the 1700s in France it was men who wore flashy clothes, had long curly hair, jewellery, high heels, makeup and perfume. In Ancient Sparta women shaved their heads and wore "men's clothes" at their wedding to be attractive to their husbands.

The gender identity of your child is a qualia for them, and only they know what it's like to be them, and they shouldn't have to claim their brain is "like a female brain" in order to be considered valid to present how they want.

Also your comment about "someone cared enough to do the research" sounds a bit patronising, because I too have done research, and the science is not settled on "female brains" vs "male brains". It's like a Venn diagram. Male brains, female brains, intersex brains, they frequently differ more widely from EACH OTHER (others of the same sex) than they differ from the different sex. I have read books from researchers on both sides, "The Blank Slate" from Steven Pinker focuses on the ways biology and broad sex differences do affect behaviour for males and females in aggregate, but that's not the same as saying an individual person has a recognisably "female" or "male" brain, as even two cis women will have differing effects of sex hormones on their brains, different levels of hormones they were exposed to in utero, in puberty, throughout their lives etc. However "Delusions of Gender" by Cordelia Fine, goes into all the ways that sex doesn't actually create as many differences in the brain as you might think, and the idea of there being a uniquely "female brain" that all women share and no men share, is just wrong. .

So yeah, trans girls, non-binary children, gay boys etc - there is an *association* between estrogen and other hormones in the womb, and the likelihood of a child being born who is trans, gender non-conforming, gay etc, but that's not the same as a causal link or a gay gene or a specific part of the brain that you can point to with reliability and say "that right there is what differentiates a trans brain from a cis brain or a gay brain from a straight brain" . Because while some trans people may have certain parts of their brain light up more than cis people in certain contexts, others will not.

My point with all this is not to undermine gender identity or presentation but to stress that it's not caused by a biological thing that can be identified, singled out and thus "proven". This shouldn't be necessary! In fact, I think the focus by certain trans activists on trying to assert that they are the exact same biological sex as a cis person and if you don't agree you're bigoted, is actually taking the focus away from what's important - letting people live and identity and present how they want in society without harm, so long as they don't hurt anyone.

And in fact, if we got rid of sexism in society, I think most transmisogyny and homophobia would go, because it's considered mostly fine for female children to dress masculine, but if someone assigned male dresses feminine, shock horror from society.

Again, I'm not in any way attacking you, I think your parenting is admirable and your child is lucky to have you. <3