I don't know if banning first cousin marriage is the right approach, because it's the reproduction that causes the problems, i.e. the aim is to prevent first cousins having babies, and a ban on them marrying wouldn't achieve that? Though I think in communities where first cousin marriages are more common, it's less likely there'd be babies born to unmarried couples, so...
And a ban on sex between first cousins would be different from other rules we have about sex which I think are mostly to do with power imbalances? Like, banning it because of "ick" or genetics is opening up a whole load of different possiblee types of sex that might be banned?
Educating about the risks maybe would have more impact - I think people just don't realise what the possible risks to any children could be, and most people would never want their babies to be born with such difficulties like what can happen in some cases of first cousins marrying.
I know first cousin married couple (I'm white as are they), their kids are healthy and happy & I could imagine that would be interpreted as proof it's safe for first cousins to have kids together. I know it isn't necessarily safe, but it's not always obvious that it isn't, on an individual level. As in, on an individual level, often it is safe? The harm accumulates over generations? But I obv don't know anything about that really. But I think education on it would be helpful.
The family bonds & community issue is pretty major I'd think. I can see it compounds risks for women, but on the other hand where there's a small community, with a v strong sense of identity/ values/ customs that aren't shared by people outside the group, it's harder to find the right partner. And some of these communities, the extended family is huge - so people have dozens of first cousins for example, potentially 100s of second/ third cousins, but not necessarily a whole lot of opportunity to make close bonds with completely unrelated people? And where there's lots of distrust of "outsiders", it might feel safer for everyone if people stick to their own.
Not saying that makes it ok, but the "yuck, incest" comments are maybe not recognising that side of it sufficiently?