The ABA Journal says, "The measure bars courts, arbitrators, administrative agencies and other adjudicators from applying or enforcing foreign law 'if doing so would violate any state law or any right guaranteed by the Constitution of this state or of the United States.' ... [and] 'No Alabama court shall be required by any contract or other obligation entered into by a person or entity to apply or enforce any foreign law.' That language could mean choice-of-law contractual provisions are invalid in Alabama courts ..."
Eugene Volokh writes in the Washington Post that most of the amendment merely restates existing legal principles, except for the part that could invalidate contractual choice-of-law clauses.
However, there are other situations where foreign law could otherwise apply, such as in a suit about a tort committed in a foreign country. And part of the impetus for such legislation is the prospect of foreign countries' notions of human rights being used to interpret the U.S. Constitution to reverse state laws or court judgments.
There are other unintended consequences that could flow from these efforts, discussed in my earlier article, "State legislation would bar foreign & religious law from American courts". Unlike most of the legislation discussed there, this latest Alabama amendment does not affect religious law, at least not expressly. Of course, especially in family law, some foreign law is religious law.
Another article, which is probably not as well researched, claims that the ban does affect religious laws. It says it was opposed by the Christian Coalition of Alabama and by ChristiansAgainstAmendmentOne.org, which claimed the ban could affect foreign adoptions, foreign marriages, and churches' self-governance.