I don't engage with people couching their transphobic content in 'think of the children' anymore so I've mostly stayed away from this and similar threads. Since the whole first page was waiting for that one person to arrive.
But I do want to comment on this.
Pink brains and blue brains have not been established to exist. So far every study which has found large structural difference between female and male brains were not natal, but after nurture both environmental interest in cultural habits and subjects of men and women, (e.g. men and women are socialized to engage in certain types of play and learning) as well as post hormone influence. So far every study which has found structural differences between male and female brains did not extend to the majority within the testing pool (e.g. not all men had specific structural differences associated with 'male' brain and visa versa for women.)
This is important because it's part of a wider dialogue about how nature vs nurture operates as a blind talking point, and in reality there is no clear white line between the two. And when nature vs nurture gets politicized, it's almost always to the detriment of a minority trying to find a magic pill to excuse who they are as 'natural' to an unbelieving audience.
But just like how there is no such thing as a 'gay gene' because homosexuality is infinitely more complex than a single gene, there's probably not going to be anything as easy for trans (and those of us who aren't trans but who have very masculinized or feminized bodies outside our natal sex) as 'your brain looks like this therefore that's your gender.' And that's okay. There's no specific place you can point to in the brain for an autistic diagnosis either, but that doesn't mean autism cannot be diagnosed and treated without a PET, fMRI or CAT. The same is true for gender dysphoria, being trans, etc.
And yet, there are differences. They may not point directly to gender identity, but there are differences.
The male brain is 10% larger than the female, though this appears to have nothing to do with intelligence.
The male brain has strong front-to-back connections.
The mail brain is more organized for motor skills.
The female brain has stronger side-to-side connections.
The female brain is optimized for intuitive thinking.
The female bfain has more grey matter.
Males are more likely to develop alcohol dependence, three times more likely to be diagnosed with antisocial personality disorder, four times more likely to have autism, and twice as likely to develop Parkinson's disease.
Females are twice as likely to have depression, twice as likely to develop Alzheimer's (in the U.S.), four times more likely to develop multiple sclerosis, and more likely to have a stroke.
Then we have to consider how some areas of the brain are responsible for certain tasks: language for example is located in Wernicke's area, a critical language area in the posterior superior temporal lobe, which connects to Broca's area via a neural pathway. Other small areas are responsible for object association, or differentiating self from non-self.
So I think it is not yet clear where (or even if) gender identity is located, but certainly we should expect it is somewhere -- because pretty much most humans do tend to identify as either male or female. That this is usually the same as natal sex, the very existence of transgendered people suggests that this might not always be the case.
I recall reading, some years ago, of a European study that found that women are sensitive to some male-produced pheromones, and so are male homosexuals. Since you can't really smell pheromones, this is directly brain-chemical function. I'll have to look that up, but again, it suggests strongly that all the answers are not yet in.