Cordelia Fine's "Delusions of Gender" does not accept differences between male and female brains.
I think there are differences in parts of the brain which are formed by hormones when in utero and during puberty which affect part of it and form a structure which is the type found in a person of the opposite sex.
This is speculation, isn't it? There's no evidence for it. Twins are exposed to the same environment in utero but there are twins where one is transgender and the other is not.
The presence of a different structure in males and females should not mean men and women should be treated differently.
In the 19th and early 20th century, when it was believed female and male brains were different, women certainly were treated differently and as a direct result of this theory. It is very naive to think that a view of female brains being different from male brains would not result in women being treated worse than men.