I don't particularly think it's especially laudable to reject the idea that male and female brains or thinking might be different for ideological reasons, but certainly in this instance there is no real evidence of the supposed hormone wash theory.
There may well be differences, as there are in other organs (heart attack symptoms are different for example), but the idea of a sexed brain always seems to revolve around stereotypes. And the idea of a 'lady brain' which was too frivolous to cope with serious matters is what kept women out of public life and positions of power for centuries. People like MA really should think about what it means to embrace sexist ideas like this.
I've never heard of a man claim he 'knows' he's a woman because he's had breast cancer, or because he believes one of his organs (his heart or liver for example) behaves more like that of a woman. It's always his brain having female attributes. Meanwhile, in most cases, his male reproductive system works just as well as that of any other man.
But the idea of an opposite sexed brain to the body is nonsense in any case. If a man's brain has attributes which it was thought only occurred in women, it doesn't mean that he has a woman's brain, but that the hypothesis that these attributes only occurred in women was wrong.