Um . . . I don't think that's it. The diversity of your genes doesn't matter much; only the possible diversity between your genes and your cousin's genes. Your cousin is still a parent's sibling's offspring; they are no further from you genetically than they would have been 100 years ago.

The real reason, I think, is decaying morality. Morality has been changing in recent decades, into something a person 100 years ago would have been horrified at. This is probably a more likely reason why many things that would have been out of the question twenty or fifty years ago are not only legal, but considered morally defensible these days.

That being said . . . . yuck.