Thanks for the explanation. I hadn't really given it much thought beyond race (ethnicity?) and gender (sex?) both being things you're born with.
I'd be surprised if most people did. I don't mean that disparagingly--simply most fields of study do not cover those topics and the vast majority of people have their "internal" identity match their "external" identity and it doesn't really cross our mind.
For what it's worth, the historical scientific philosophy was that of tabula rasa and a strong prevailing theory was that concepts of gender identity were all learned from society and upbringing. The aforementioned case study (David Reimer) arose when a doctor who performed a botched circumcision encouraged the parents of the child to simply raise the infant as a girl. Unfortunately, the child grew up with a lot of stress and anxiety for they never self-identified as a girl despite the parents never informing him he was born a boy and could not reconcile his personal feelings with how he was told to behave. When he finally learned the truth, he started living as a man (though, he eventually committed suicide because of the anguish he had experienced).
The case is, in the psychology field, extremely famous for becoming the foundation of modern gender identity theory as well as being a benchmark in transgender studies.
If someone hasn't studied psychology, however, I'd be very surprised if they had heard it. I know I didn't until I took my classes.