"Mongoloid" is both offensive and inaccurate. The term was used for babies with Down Syndrome, which is not a risk especially linked to in-breeding. And #2 has the right of it, the risk for cousin marriage genetically depends on the group the cousins are from. It can be safer than somebody else marrying someone with no clear relation, but part of the same small genetic group. Or, if you have known genetic health issues or nasty recessives in your family, it can be particularly problematic if you have kids. Of course, not everyone who marries wants to have children or wants to have children with their own genetics.

I also think genetic issues is a terrible reason to deny a marriage, since there are people with known serious dominanbt traits, who will have a 50% chance of passing it on to any child of theirs if they mate with somebody who doesn't have it, so that's the best case. And we don't deny them marriage or the choice to have kids. I think denying it to them would be a much worse problem. And if we're okay with 50% known serious risk, then it seems rather stupid to not allow the significantly smaller risks that the average set of first cousins would have.

Incest is a problem due to the potential power imbalance, which can lead to a lack of true consent. But usually first cousins are raised separate enough that they can both consent, and there's no indication that they aren't both adults. Obviously if there is some sort of coercion on one of them to marry the other or one is a child then that would not be at all acceptable.

@15,17 Selective breeding is in the bible.

One would think that it isn't a huge step from that science to evolution, but at that point we're thinking...