I've heard it explained that brains of lesbians and gays are sort of shifted towards the middle. So there are feminine / masculine aspects to them that are not conforming with their sex, but that is different to saying that they have brains that are very much like or identical to the opposite sex. Interestingly, we know that there is a high correlation (not exact) between gender non-conforming behaviour as kids and homosexuality, so there does seem to be something to it. And there does seem to be gender different behaviour in young kids / babies e.g. girls cry more than boys, girls like pretty things and social play, boys prefer rough and tumble play and to pull things apart to see how they fit together and work.

I think it's worth mentioning though that there aren't massive differences between male and female brains. And then you have complicating factors such as non-neurotypical conditions (e.g. autism, add etc.), and speculation over how much is nature vs. nuture given that girls and boys often lead very different lives. We may know that there are neurological differences between baby girls and boys, but how much of that carries over into their development into adults?

Edit: as a disclaimer I should probably say that I didn't do science in high-school and most of what I know from the topic I learn from google.