I was actually the source that Jess was referring to, Tracey Folly, having posted a link not long ago to Genius Turner noting that the taboo against first cousin marriage is a peculiarly American institution — for the most part.
Geneticists don’t actually think there’s a real problem with first cousin marriage. There is a slight risk of genetic unmasking of unfavorable traits, but that risk is so low scientists say it is insignificant.
Every individual should certainly make their own informed choices about what risks they are comfortable with. But the social disdain we Americans reserve for first cousin marriage is undeserved according to people who study the issue.