Dark Question: Lets assume that there is a 100% proof positive way to identify people with pedophilic tendencies using genetic testing.

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.

Most offenders are not pedophiles.

No, keeping a registry and obligatory treatement is enough. No need to kill based on attraction alone.

I consider normalization of child abuse as crossing the line and it seems most in this website who did so through written content were not punished by the law.

I find it difficult to engage in imaginary scenarios as if killing them is a real concern when reality reflects the complete opposite.

No. Some people don't act on it, and try to get help. So wouldn't be fair to persecute people for their illness.

So Eugenics?

I will stop at "identify" such people, at the least to have treatment available to them. There's no need to "apprehend" until you know a crime has been committed.

And I don't agree with capital punishment for the most part (innocent people can sometimes be executed, which is the main reason capital punishment is in invalid, not because an actually guilty person does not deserve it). To the degree I agree with capital punishment is for cases where the guilty are committing acts that are existentially detrimental to most inhabitants of this planet or a large group of people. Genocide and destroying the climate to make the planet uninhabitable are existential threats to a lot of people. While pedophilia sucks, its effects are limited to a smaller number of victims, and once caught the person can be kept imprisoned permanently if necessary to prevent further attacks.

Now as for pedophiles who have not yet been born, and the science was foolproof in detecting them with a 100% accuracy rate over a long period of time, then potentially adjusting them before birth or terminating the pregnancy ... or just completely weeding the flaw out of human DNA prior to any conception at all or preventing the conception, that would fine by me, whether you call it "eugenics" or not.