The origin is indeed the core issue.
IMO, behavior is their concern. The only time it becomes our concern is when that behavior becomes public or they insist we treat them as of the opposite sex; or they insist we spend our tax dollars via the schools to promote our acceptance (there are likely more, but those jump out).
Again, the one eye blue and one eye green scenario, biological mistakes happen.
The born homosexual looks in a mirror and states "that is a mistake". Imagine society trying to convince that individual they actually are of the opposite sex. The success of the argument will, IMO, depend on significantly more than a verbal discussion.
Finally, as I noted upthread, I am confident a large segment of the "born" group, if not all, would seriously consider taking a "magic pill" (or any other demonstrably successful therapy), if they were reasonably certain it would resolve their dilemma.
But this is precisely the issue, if you are asking what society should do. Society doesn't need to do anything unless their behavior presents a threat to norms.
The born homosexual….
I don't believe there is such a thing. And I have the pleasure of acquaintance and friendship with many gay men and a few of other stripes.