Assuming that it was in fact genetic, eliminating them all from the population would in theory wipe out those genes from the population. I'm just not so sure that it is genetic and that even if it was, those genes don't necessarily have to activate. Some people are genetically predisposed to alcoholism or other diseases but manage to dodge those bullets.
But assuming this was foolproof, it does have some Nazi-ish undertones. Eliminating people based on their inferior genes was a big deal for Hitler. If we select for one sexual orientation, what's to stop them from going after LGBT next? Or going after people with other unfavorable genetics? Once you open that Overton window, there might not be any way to shut it.
In the end, our religious and legal systems tend to stress that we have free will. If we do something like this, we're admitting that people don't have free will, and that could usher in the way for authoritarian dictatorships. People will become slaves to their genetics, and you'd end up with something akin to Brave New World or Gattaca. We'll have a caste system based on genes since that is now the basis for the value of your life.
