As I noted below, the Tenth Circuit U.S. Court of Appeals has upheld the injunction ordering the Oklahoma Secretary of State not to certify the enactment of the Oklahoma anti-foreign-law/anti-Sharia constitutional amendment. But here's an interesting twist: Though the high-profile part of the amendment banned Oklahoma courts' use of Sharia law, the amendment more broadly banned the courts from using foreign law:
The Courts provided for in subsection A of this section, when exercising their judicial authority, shall uphold and adhere to the law as provided in the United States Constitution, the Oklahoma Constitution, the United States Code, federal regulations promulgated pursuant thereto, established common law, the Oklahoma Statutes and rules promulgated pursuant thereto, and if necessary the law of another state of the United States provided the law of the other state does not include Sharia Law, in making judicial decisions. The courts shall not look to the legal precepts of other nations or cultures. Specifically, the courts shall not consider international law or Sharia Law. The provisions of this subsection shall apply to all cases before the respective courts including, but not limited to, cases of first impression.
As I mentioned before, this was a very bad idea, for reasons quite unrelated to the Sharia law question: Whatever one may think of the propriety or impropriety of courts using foreign law or international law as a guide in interpreting the U.S. Constitution, foreign law is and should be routinely considered in a wide range of contract, tort, property, and family law cases; see here for some examples.