> My guess is it’s neurological, since there aren’t discernible hormonal, genetic, or anatomical differences between trans and cis people.

That's exactly the point. If someone's "gender identity" doesn't refer any observable characteristic other than their "gender identity", then the entire concept is circularly defined and therefore meaningless. It's like if I were to say my biological height is 5'7" but my "height identity" is 6'3". What meaning does "height identity" have and why should anyone take a concept like this seriously?