That’s the issue lurking in In re Aramco Servs. Co., now on appeal to the Texas Supreme Court. DynCorp and Aramco Services (both of which were at the time Delaware corporations headquartered in Houston, though Aramco Services is a subsidiary of Saudi Aramco, the Saudi government’s oil company) signed an agreement under which DynCorp was to create a computer system (in the U.S.) and install it at Aramco’s Saudi facilities. The contract provided that it was to be interpreted under Saudi law, and arbitrated under Saudi arbitration rules and regulations. Those rules and regulations apparently call for the arbitrators to be Muslims or Saudi citizens [UPDATE: I originally erroneously said "Muslim Saudi citizens"; I've just corrected it]. The trial court, however, appointed a three-arbitrator panel consisting of a Muslim (apparently a Saudi) and two non-Muslim non-Saudis. Aramco appealed, arguing that (1) under the contract the arbitrators were not supposed to be appointed by a court, and, (2) in the alternative, that the court erred in appointing non-Muslim non-Saudis.
The Texas Court of Appeals agreed with Aramco on item 1, and therefore didn’t reach item 2. But there is an interesting constitutional issue lurking in the background: If a contract does call for a court to appoint arbitrators, and provides that the arbitrators must be Muslims (or Jews or Catholics or what have you), may a court implement that provision, or does the First Amendment or the Equal Protection Clause bar the court — a government entity — from discriminating based on religion this way, even pursuant to a party agreement?
I’m inclined to say that the court indeed may not choose arbitrators based on their religion, even pursuant to the agreement. First, that would be discrimination based on religion by a court; nor can one say that any rights against such discrimination were waived by the contract, since the discrimination is against nonparties to the contract (the arbitrators). Second, it might impermissibly entangle the court with religion (in violation of the Establishment Clause nonentanglement doctrine, which is separate from the First Amendment nondiscrimination doctrine), since it would require the court to decide who is really a Muslim; I say “might” because it’s not settled whether this second objection would apply when there’s no dispute about whether a person is a Muslim.
There is an interesting analogy, though, that might cut the other way for some people: Wills that provide that property be distributed only to descendants who continue to adhere to a particular religion, or who are married to people in that religion. (For an example of a case dealing with this, and refusing to enforce such a will, though on a 2-1 vote, see here.) There too a court is asked to select people based on their religions, pursuant to a nongovernmental entity’s choice; and though the selected person in the will case gets the property, rather than choosing who gets the property (as in the arbitrator selection scenario), I don’t think that this is a material difference. I think that applying religion-discriminatory provisions in a will should be unconstitutional when done by a court, but my sense is that many others might disagree with me, precisely because the religious discrimination stems from a private party’s initial decision (even if it’s implemented by a court) and not a government entity’s initial decision.
If the parties want arbitration by Muslims (or, again, Orthodox Jewish rabbis or Catholic priests or whoever else), I don’t think there’s any public policy objection to such a provision, or to judicial enforcement of the arbitral result. (I set aside for now possible concerns about discrimination based on sex or religion in the consideration of evidence by arbitral tribunal applying rules calling for such discrimination, concerns that might not arise in particular arbitrations, and that might in any event not be seen as dispositive.) But the arbitrators would have to be chosen by some entity designated in the contract, an entity that is not an American government actor. Likewise, in the will scenario, the testator could certainly himself choose beneficiaries based on his view of their religiosity, and can also delegate this decision to a private person or organization appointed by a will, such as a trustee or someone vested with a power of appointment.
I also don’t think there’s any problem with enforcing a requirement that the arbitrators be Saudi citizens, even if that in practice means they’re going to be Muslims. Discrimination by American government agencies based on citizenship status is often permitted — absent some federal preemption of state practices in this regard, preemption that I doubt would be found here — and checking someone’s citizenship status does not raise the entanglement-with-religion concerns that I mentioned. But discrimination by American government agencies based on religion is almost never permitted, and the same is true for decisions by government agencies about who is a Muslim (outside a very few contexts where the no-entanglement rules are broadly relaxed, such as for prison chaplains and military chaplains).