Right, EXACTLY like was stipulated IN THE CONTRACT - a contract that was signed by both parties. The parties agreed to be bound by arbitration, arbitration in this instance that applied Sharia law. If one of the parties didn't want to be bound by arbitration, then they shouldn't have signed the contract, right?
This is an incredibly typical motion, where the winning plaintiff asks the court to enforce the order of the arbiter. The only thing that makes it "unusual" is the fact that it's a Sharia arbiter.
"The court held that it will determine whether its interpretation of the Qur’an’s dispute resolution procedures were followed."
Right, the court will determine if the agreed upon arbitration procedures were followed. It does not review the decision that the arbiter came to, hence the term binding arbitration.
"If parties contract for religious doctrine to govern their relationship, do you believe it is within our courts’ jurisdiction to review and interpret the applicable religious doctrine if one of them sues in court?"
It's irrelevant because that's not what happens in binding arbitration. That word "binding" means something. It means the decision of the arbiter is set-aside from judicial review. What is subject to judicial review is the arbitration procedure. In this instance, it just happens to be a religious court acting as arbiter.
"Or, is the choice of law provision also a choice of venue clause, in the sense that the parties are forced to go before a religious tribunal or private arbitrator if they’ve chosen religious law to govern the contract?"
The "venue" in this particular context is arbitration. The choice of law provision (in this context) addresses the law that the arbiter applies.
However, I would point out that it's conceivable that some religious-based choice of law provisions are applied in a secular court of law. Usually, these applications happen in the context of divorce decrees or probate court. A last will & testament might stipulate that the decedent's assets are distributed to heirs using a religious law doctrine. The probate judge will then follow that doctrine when dividing and distributing assets. This is incredibly common in NY amongst all the varying orthodox Jewish sects. It happens literally every day.
Keep in mind, these are all civil law law applications, almost always as those laws relate to contracts, or wills. Sharia or Jewish laws, and foreign laws are not applicable or relevant to our state or federal criminal laws in any way.
Isn’t it the case, though, that motions to confirm arbitration awards are generally decided according to the Federal Arbitration Act, or according to the state law of the forum? Why would it be appropriate for the court to eschew those laws and decide the motion to confirm according to Islamic law instead? Even if the contract said that the confirmation of any resulting award was to be determined according to Islamic law, how does the court have jurisdiction to review, interpret and apply religious doctrine? Supreme Court precedent says courts have no jurisdiction to resolve issues of religious doctrine. And, parties cannot, by contract or otherwise, confer subject matter jurisdiction on the court.