I suggest that some people read up on basic genetics.
It all depends on the gene pool. If first cousins have married for several generations there is an increased risk.
Everyone have damage to their genes. The reason why one shouldn’t have children with close family is the possibility that the damaged genes match, and the offspring will develop a disease or syndrome. However, a third cousin is related through your great-great-grandparents (Graphic), where they on every step on the way (supposedly) met unrelated mates, whose dna make up half of every childs genetic make up.
If you look at it mathematically, it is exponential in nature.
This cousin stigma is quite american I might add. In Europe there is no prohibition against first cousin marriage, though it’s not encouraged. In most countries in the world this is not an issue.
Arguing that one should refrain cause of genetic reasons, shows only that one is uninformed. A third cousin is just as perfectly suited to be a spouse as anyone else.