You are right, I think, to root the conflict in religion. The dominant religion in the West, Christianity, treats the human body as a given. That is to say that while you are more than just your body, you are certainly not less: there is a union of mind and body that separates only at death. If they disagree, a reconciliation must be attempted from the outside (i.e., by God).
Of course today we have technology that puts a veneer of science on what is really a religious idea: we are essentially our mind and not our body. When the two disagree, we needn't change our minds because we can alter the body through hormones and surgery.
On the face of it, I don't see how you could reconcile these two positions. I think the use of genetic predestination was used as an attempt to do this: if I'm made this way then how can it be wrong to be {gay, trans, etc.}? But in general I think the denominations that were predisposed to blessing homosexuality (for example) were unlikely to need scientific persuasions like that. When it became clear that rigid denominations weren't going to budge, it feels like genetic predestination became unfashionable.