Re Richard Dawkins. He must get it. He has endorsed Helen Joyce's book, been commenting on 1984 and language fuckery and made the Rachel Dolezal comparison, now he is fending off alt right accusations and realising the full extent of this ideology. he is probably sensible to not completely alienate the SJW's since he will have a lot of influence on floaters.
Re: the intersex brain theory.
I think that some of this comes from the Le Vay INAH3 studies and the spin off studies by Swaab, Byrne etc. They found a reliable sex based size and density difference in the nucleus, It could be reasonably considered a primary sex characteristic however they also found a statistically significant contralateral relationship between straight and gay subjects and expected INAH3 size. So the most compelling hypothesis is that it is responsible or contributes to sexuality not gender, but to me it backs up Blanchards transsexualism typology.
When they studied trans people they found INAH3 corresponded a bit with the sex they aligned with not their natal sex. However they failed to factor in the sexual orientation of the trans people (they were all straight (androphilic) trans women or same sex attracted. They were also on cross sex hormones.
There have also been twin studies comparing identical and fraternal twins and transexuality.
I think relative levels of prenatal Testosterone exposure or insensitivity to it are thought to contribute, to relative masculinisation/ feminisation and that it could be maternal hormones not the foetus's.
This doesn't even begin to explain late onset Gynephilic mtf transexuals, ROGD and it sure as shit doesn't explain non binary identities.
It does seem likely that intrauterine hormone exposure has some effect on sex characteristics, preferences and behaviours, but it only proves the existence of masculine women and feminine men, not inate gendered souls or intersex brains.
Even if it were proven beyond a shadow of a doubt that the INAH3 or some other structure or combination of structures is responsible for gender identity and that gender incongruence is a tangiable thing, not just a tendency towards the feminine, need to be able to describe ourselves as a sex group based on reproductive role, not how female we feel.