Gender realism/essentialism considers gender to be primarily a matter of biological sex, although there can be cultural variations in how to define, express, and encourage masculinity and femininity. Fundamentally nature with some nurture overlay. Gender nominalism views gender as a product of social conditioning. Nurture rather than nature. At least, those are the rough-cut definitions I'm using.
Another approach by the transgender lobby is to define gender as a psychological rather than physical condition. Gender is in your mind. There's a grain of truth to that, but it's supposed to be correlated with our bodies. Otherwise, it's delusional.
Since so many of the finespun distinctions which the transgender lobby draws are imaginary, the definitions are endlessly protean, since they're not constrained by biology, but ideology.
There's extensive anecdotal as well as sociological data that men and women stereotypically have distinctive interests and cognitive abilities. Overlap doesn't eliminate the distinctives. It just means men and women belong to the same natural kind: humans.
There's the feminist/transgender theory that it's all socially conditioned, but despite aggressive efforts to "level the playing field" and overcompensation, the stereotypical differences remain.
I've probably read two or three liberal writers who used to believe boys and girls were naturally psychologically interchangeable. The differences were due to sexist socialization. That's until they had kids of their own, and the stereotypical differences began to surface with a vengeance, so they changed their mind.
From theological perspective, gender is grounded in God's natural design for manhood and womanhood. We could also add the possibility of naturally gendered souls. Indeed, I suspect that has a basis in fact. However, embodied experience in a male or female body will also have a conditioning effect on the mind or soul (I presume).