I basically abstain on politicization of incest. I've never once met someone that desires incest, never once seen someone argue in favor of incest, never seen news about a march on Washington of people that want incest marriage legalized, etc. Maybe there are people out there that advocate such things but I've not seen them. Most articles I've seen about incest being a problem have to do with child victims, which I'm obviously against. So I've not seen reason why incest of adults should be on my political radar at all.
I certainly don't think it's fair or ethical for people with significantly similar DNA to have children with each other, as that is basically a type of child abuse, since they're setting up a scenario with a very high likelihood of physical problems. But I wouldn't go so far as to say I'm against allowing genetically unfit children to enter society, like the wording of the OP. That would mean I'm against people with Down Syndrome and other genetic abnormalities that have nothing to do with incest from being accepted, which I'm not.
And if the idea of moral degradation of society is being brought up as a claim about the reality of the situation, I'd need to see a specific starting point and ending point along with a geographical location to be convinced. In other words that argument needs to be more tightly defined. Because history of the USA includes slavery of people of African descent, slaughter of Native Americans, barring women from the right to vote, a bloody civil war, etc. So to say that there is moral degradation- I'd certainly need to see a more precise description of that claim if it's relevant here.
One thing I remind myself about legalizing or criminalizing things is that if things are made illegal, then eventually, people have to be willing to back that law with physical force. Ultimately that's what law is, even if it's a minor law that starts with a fine or something, because refusal to adhere to it or answer minor penalties cascades up the ladder of severity until physical force is on the table as an option. Otherwise, it's a suggestion rather than a law. Am I willing to send force to stop closely-related consenting adults from being intimate with each other on their own time without the desire to have children? Not really, no.
The problem is how to enforce things, how to make laws that can be enforced like disallowing the existence of children with incest. Who to penalize, and how. A non-enforceable law is not worth much unless it's just a political statement.
