There is probably some truth in trans brains being different [...].
My understanding is that adult male brains are 10% larger (unsurprising, since adult male bodies - and their internal organs generally - are also 10% larger). [Side note: no evidence that this gives men any intellectual advantage :o) ] However, although there are other sexed differences that develop in male and female brains after puberty there is no evidence to support the claims that male-to-female transsexuals have brains that more closely match adult female brains. There are huge caveats, of course: 1) a general lack of data, not least because TRAs have tried to stop it being collected, as a pp has noted above; 2) specifically, it is unclear how the brains of mtf individuals participating in studies have been affected by cross-sex hormones in the first place, thereby blurring cause and effect.
Helen Joyce addresses this somewhat in her book Trans: When Ideology Meets Reality in Chapter 3, where she writes:
Once the activists are done with demoting sex from an objective characteristic of individuals to a social fiction, it is time for step two: to ‘reify’ gender identity – that is, to turn it from an abstract idea into something concrete. The main argument put forward is that neuroscientists have found a brain structure that is different in trans people, or shown that trans people’s brains look like those of the sex with which they identify.
This is an odd claim to make if you also insist that biological sex is not binary, since you have to know which bodies are male and female before you can group brain scans into male and female and look for the differences. It is equally strange to claim that differences between brains could be a solid basis for classifying people as men and women, but those between genitals could not. Machine-learning algorithms can be taught to classify brain scans as male or female with around ninety-five percent accuracy. But that is far worse than the human eye can do with faces, and worse still than it can do with genitals.
Helen's book is brilliant - no wonder that the TRAs hate her so much.