I have no problem with people and businesses utilizing private arbitration of whatever kind to resolve disputes, so long as they choose to be contractually bound by the rules and outcomes of the arbitrator and so long as the real courts do NOT give the force of law to illegal contracts. One cannot create an enforceable contract whereby one person permits another to commit a battery or "give" one's child in marriage before the child is of legal age, for example. The decisions of private arbitrators should never be a defense to violations of civil or criminal law.

I would guess that the would-be divorcees who submit to these courts do so in order to get the blessing of their families to proceed with the divorce. With the approval of the Sharia court, a Muslim woman has a chance to get a divorce and move on with her life. Without it, I suspect she is likely to be ostracized or worse. It seems to me to be similar to a Catholic seeking an annulment.