Dhyer: they could raise it as a defense in their criminal prosecution but it would fail. Let's take a gander at the bill, shall we:
Here's the meat of it:
46 (a) A person's civil right to exercise of religion shall not be burdened even if the burden
47 results from a rule, law, ordinance, regulation, or policy of general applicability unless
48 demonstrated, by clear and convincing evidence, that application of the burden to the
49 person is in furtherance of a compelling governmental interest and is the least restrictive
50 means of furthering that compelling governmental interest.
All the bolded terms have special meanings.
14 (1) 'Burden' means any government action or implementation or application of any law,
15 including, but not limited to, state and local laws, ordinances, rules, regulations, and
16 policies, whether statutory or otherwise, that directly or indirectly constrains, inhibits,
17 curtails, or denies the exercise of religion by any person or that directly or indirectly
18 pressures any person to engage in any action contrary to that person's exercise of religion,
19 including, but not limited to, withholding benefits, assessing criminal, civil, or
20 administrative penalties, and exclusion from government programs or access to
21 government facilities.
So "burden" here includes any government act whatsoever including the application of criminal laws that have no direct bearing whatsoever on religion.
24 (3) 'Exercise of religion' means the practice or observance of religion under Article I,
25 Section I, Paragraphs III and IV of the Constitution of this state and the free exercise
26 clause of the First Amendment to the Constitution of the United States, including, but not
27 limited to, the right to act or refuse to act in a manner substantially motivated by a
28 sincerely held religious tenet or belief whether or not the exercise is compulsory or a
29 central part or requirement of the person's religious tenets or beliefs.
As you can see, "exercise of religion" is defined extremely broadly. Your religion need not compel you to act in a certain way; it only need lightly suggest that you act that way.
22 (2) 'Compelling governmental interest' includes, but is not limited to, protecting the
23 welfare of a child from abuse and neglect as provided for by state law.
This is all this particular bill has to say about what the term "compelling governmental interest" means. However the language "least restrictive means of furthering a compelling governmental interest" is well-understood in US jurisprudence to mean that in determining whether a law or governmental act is valid the court should be very willing to strike the law down. Typically strict scrutiny is applied to laws that burden people unequally on the basis of race, or infringe on a fundamental right protected by the Constitution. Ah, but life is one of the fundamental rights protected by the constitution, so even applying strict scrutiny to the application of a law against murder to an honor killing motivated by sincere religious beliefs, the law against murder stands.
Ah, but what about marrying your niece? Does your foreign culture, which happens to heavily feature religion, tolerate such marriages? Even if it doesn't, do you have it in your misguided head that it is OK, perhaps because someone in the old testament did something like that? Looks like you are acting in a "manner substantially motivated by a sincerely held religious tenet" even though your religion probably doesn't make marrying your niece a "central part or requirement" of your religious practice. Hey, you've got a bona fide "exercise of religion!" And incest is against the law, so there's your "burden!" Now, does the government have a "compelling governmental interest" in stopping you from marrying your niece such that it still can do so? Probably not, unless your niece is a minor. Certainly no one is having THEIR fundamental rights violated by you marrying your niece. But what about the fact that it's illegal to marry your niece pretty much everywhere, and science shows that having babies with someone so closely related to you vastly increases the chance of birth defects? What about deep concerns that a person in position of authority like an uncle would exert undue influence on their brother's daughter? Well, those sure are good points, and maybe you could say they demonstrate a compelling government interest, except...
61 In determining whether a compelling governmental interest is sufficient to justify a burden
62 on a person's exercise of religion pursuant to subsection (a) of Code Section 50-15A-2,
63 only those interests of the highest order and not otherwise served can overbalance the
64 fundamental right to the exercise of religion preserved by this chapter. In order to prevail
65 under the standard provided for by subsection (a) of Code Section 50-15A-2, it shall be
66 demonstrated that such standard is satisfied through application of the asserted violation
67 of this chapter to the particular claimant whose sincere exercise of religion has been
68 burdened. The religious liberty interest protected by this chapter is an independent liberty
69 that occupies a preferred position and no encroachments upon this liberty shall be
70 permitted, whether direct or indirect, unless required by clear and compelling governmental
71 interests of the highest order.
Yeowch. Looks like your niece is out of luck.