Your original premise, “Man is born a sinner,” could have several interpretations. My own would be that “Man is unworthy of God without redemption.” But let’s let that pass.
Could a person be born gay? Possibly. Kinsey thought there was a continuum from 100% straight on one end to 100% gay on the other, and most of us were somewhere in between. I think from everyday experience that makes sense.
However, until science proves there is a “gay gene,” I personally think it has more to do with your environment growing up and choice.
If you look at history and anthropology, you can see that entire societies (ancient Greece) were “gay” in the sense that homosexual sex with boys was not only common, but was applauded. So because it was accepted–and even expected–it was done. There was even the “Sacred Band,” an elite military group of 300 in Thebes made up of 150 homosexual couples. The famous line in Leviticus wasn’t put there because men weren’t having sex with each other–obviously they were, and the verse was forbidding it. Different societies have had vastly different levels of acceptance of homosexuality.
Turn to anthropology. In Papua there are several tribes where homosexuality is simply a stage between boyhood and adulthood. Then there are English boarding schools, prisons, and yes (sorry) Muslim societies where a lack of women is made up for by the availability of men. You could certainly argue that in these cases it’s not “really” a choice, it’s more a matter of convenience, but it’s still there, and to me it’s obviously a choice, although not a totally free choice (but what is?). And generally it’s seen as a stage in a “normal” man’s life.