For crying out loud to you! Brains are intensely plastic. By the time someone is old enough to get Alzheimers they have been exposed to decades of genderized experiences, beliefs, and opportunities. To imagine that has absolutely no effect is to not understand how brains (or society) works.
What part of this paragraph from Scientific American doesn’t make sense to you?
“Brain differences are indisputably biological, but they are not necessarily fixed, or hardwired. The crucial, often overlooked fact is that experience itself changes brain structure and function. Neuroscientists call this shaping plasticity, and it is the basis of all learning and much of children’s mental development.”