The risks are not "minimal". There are increased risks in cultures where first cousins marry. Part of that is that married first cousins have an increased risk of having children with birth defects. And part of it is that people are more related than they think if everyone is marrying a first cousin.
While I don't necessarily agree with, say, sibling marriage, the argument about birth defects is not very compelling. This ruling pointed out at one point that an ability to procreate is not a requirement for marriage in any state. Further, genetic testing to avoid birth defects is not a prerequisite for marriage, so why would sibling marriage be precluded to avoid birth defects. Should society therefore only allow siblings or cousins of the same sex to marry because they can't procreate?
Thank you for pointing that out but I still maintain it's irrelevant. People that will pass on genetic issues to their children are not banned from getting married nor banned from having children. On top of which as science progresses it's likely all those issues can be fixed. In other words, it's not a valid reason to deny siblings getting married.
The link I posted earlier deals with this.