No, you're confusing brain shape/type with neurology.

Neurology is the way neurons connect with other neurons to form our consciousness. Some things are dynamic, such as memories.

Others are flexible but can change over time, such as tastes and preferences, political opinions, etc.

Others are more rigid, such as our sense of identity, which includes the gender identity that gives us the sense of "wrongness" when we are misgendered (though some people are genderfluid, and this identity is in flux, though still not under the person's control).

It is known that neural connections develop differently in men and women. There is obviously a great variation between people, so it's a hard topic to study, but gendered patterns have definitely been observed.

It has been suggested that a missing testosterone surge during a specific point of embryo development may be a cause for a different development path, but last I saw of this it wasn't well researched.

As for trans men and non-binary people, the causes are even lesser known, but the research on the resulting gendered patterns is pretty solid.