Dahlia Lithwick at "Slate" discusses the recent blog panic over the fact that Yale Law School dean Harold Koh, who will be appointed to an administration position may have said that Sharia law could be applied by a US court in an "appropriate case."
This is a relatively noncontroversial legal idea, and the people pretending it's radical are probably being dishonest. However, it seems likely that Koh's statements about US courts interpreting Sharia law are confusing to people unfamiliar with legal practice.
Law varies from state to state, because states' legislatures and court systems are independent of one another.
The governing law of, for example, New York and New Jersey may result in different outcomes. Of course it goes without saying that the governing law of New York and Argentina might instruct different analyses or reach different results.
When a lawsuit is brought in a court, the law of the place of the suit will generally govern, and the defendants can try to object to that in a number of ways. But parties to a contract can agree that any arising disputes will be governed under a certain set of rules.
Federal and state courts in the United States routinely try litigations arising out of foreign-law contracts, and judges apply the foreign law that is applicable. US contract law is that the intent of the parties should govern, and that, accordingly, such choice-of-law clauses are generally valid.
Application of foreign law to such contract disputes is extremely commonplace and uncontroversial. Similarly, even where there is no choice-of-law clause, courts may voluntarily determine that the facts of a case fairly require the application of foreign law, and apply it. This is one check on a plaintiff's ability to choose the jurisdiction where the lawsuit occurs.
Sharia law would just be another set of rules to apply, and no different than any foreign law. My understanding is that, in Europe where there are much larger and less-integrated Muslim populations, Sharia-governed contracts are quite common. Additionally, there is a push in Europe to make Sharia family courts available so that Muslim women can seek divorce and protection from abuse in a fair forum.
It's not inconsistent with any US law to apply a foreign set of substantive rules on the agreement of the parties. Certainly, neither Koh nor anyone else is suggesting that Sharia criminal courts be established in the US, or that non-Muslims who have not entered into Sharia-governed contracts should have Sharia foisted upon their ordinary state-law disputes.
This is a total non-issue.