If you want a look at pure cultural defenses that do set up a separate legal rule for people who belong to a particular group, check out Rhode Island General Laws § 15-1-4:
The provisions of §§ 15-1-1 – 15-1-3 shall not extend to, or in any way affect, any marriage which shall be solemnized among the Jewish people, within the degrees of affinity or consanguinity allowed by their religion.
The Rhode Island law dates back to the colonial period. In a similar vein, Colorado and Minnesota follow the Uniform Marriage and Divorce Act in exempting uncle-niece marriages that are “permitted by the established customs of aboriginal cultures.” The Commissioners’ note to the Act says that “The intent is to save those special customs of Indian tribes, of Alaskan natives of various ethnic origins, and of Polynesians, which may not accord with the incest taboos of Western culture.”
Note that the Rhode Island law is not a standard religious accommodation for religiously mandated or motivated behavior; I don’t believe that Jews of the era saw themselves as having a religious command or suggestion to marry their nieces, and of course many didn’t. Rather, Jews thought such behavior was permissible — since the Leviticus 18 incest prohibitions don’t include uncle-niece relationships — and for social reasons thought it was sometimes useful. (I’ve heard as explanations the desireto keep family wealth in the family, and the small number of prospective eligible mates stemming from the small size of the community.) And I assume that the Rhode Island legislators thought the law sensible because they saw the incest ban as primarily a religious purity rule, rather than an attempt to prevent secular harm, and because they thought Jews’ contrary religious understanding deserved respect (perhaps precisely because that understanding was based on the Old Testament).
Nor are the aboriginal culture exceptions like the various special rules relating to Indian tribes, which have been justified on the grounds that the tribes have separate political existence. The exceptions apply regardless of whether the person is a member of a tribe.
So these strike me as truly separate rules for what are seen as separate cultures. I think they’re a bad idea, and probably a violation of the Equal Protection Clause, especially to the extent that “the Jewish people” and “aboriginal cultures” are understood as ethnic categories, or closely linked to ethnic categories. But if you want to see (rare) examples of true cultural defenses under American law, here they are.
UPDATE: Some commenters came to this post expecting to see more on incest generally; you can see that in the post about how the law should treat incest, and, indirectly, in the law and morality post. This post is part of a series on cultural defenses generally, not limited to incest.