I'm prepared to believe there's a reality to the biological sex of brains - probably heart size, lung capacity etc too - the same way there's biological reality to chromosomes, reproductive organs, physical size such as femur length, skull formation and pelvic formation, hormones, and ability to pass on DNA via reproduction. As far as I'm aware at present all the above can be seen on sight and on scans except brain.
Biological sex is objective fact irrespective of time, culture or place, and across the globe female humans are oppressed as a result of their biology. Roles, stereotypes, expectations etc are fluid, cultural and very highly varied. How one sex treats the other is based on the society, politics, language, social constructs etc.
Having a female sexed body does not create a biological imperative to perform what UK society has labelled as 'feminine interests', and has embodied and associated with weak, silly, inferior, less intelligent, vulnerable, etc etc etc. In matriarchal societies where women are expected to be the hunters and decision makers, they don't have a biological compulsion to wear pink and teeter on high heels. The biological imperatives for both sexes are around reproduction, based on reproductive capacity.
The pink/blue brain theory is an attempt to validate the claim that performing femininity or masculinity is a biological imperative. It clearly isn't. There have always been feminine men and masculine women.