Cousin marriage was legal throughout the USA until the 1860's, and is still legal -- sometimes with restriction, but mostly without restrictions--- in the majority of states. It is also legal throughout Canada and Mexico; in fact, the US is the only Western country that has any restrictions on cousin marriage at all.
So it's just factually wrong to see cousin-marriage is a distinctively Islamic thing, although Muslims (especially the Arab Muslims) do socially favor it to a high degree, whereas in the USA, even where legal, we tend to socially disfavor it.
Cousin marriage is only one of the problems; it has been allowed in non-Islamic cultures at various times, particularly in Protestant cultures (on the other hand, you had to get a dispensation in the Catholic Church because the general rule was that a first cousin was out of the running).
The other problem is polygamy, which does bad things to the gene-pool because you have a large local concentration of people with the same father. He, in turn, has at least some wives who are probably closely related to him because of the effect of not prohibiting cousin marriage and permitting polygamy.
The Jews, like all other primitive peoples, were polygamous, and God essentially brought them to monogamy. The Greeks and the Romans also abandoned polygamy, and one of the great strengths of Western culture was probably the establishment of monogamy, which meant not only better conditions for women, but more dedication on the part of men to their offspring, more traceable inheritance routes, and better, albeit unconscious, genetic selection.
I think people often discount the “side-effects” of religious practice and law. Islam is a perfect example of how a false religion can poison its entire environment.