Muslims in different parts of the world, especially in majority non-Muslim countries, are encouraged to run their own Muslim courts and Muslim judges to the best of their abilities. They should seek every legal channel to establish their presence. In addition, Muslims should try their best to have their own arbitration and judicial systems. In case a Muslim judge is appointed by a non-Muslim country to settle the issues pertaining to Muslims, Muslims have to abide by his jurisdiction as long as it conforms to the rules of the Shari`ah.

SalehibnFawzan Al-Fawzan, a prominent Saudi scholar, states the following: If a Muslim judge is appointed by a non-Muslim country to issue judgments for Muslims in accordance with Islamic law, then it is obligatory for Muslims under his or her jurisdiction to abide by his or her rulings. Arbitration among people is something essential in order to protect and safeguard people’s interests.
This is something quite valuable for Muslims who live in non-Muslim countries. They would have to arbitrate to him or her and abide by his or her rulings as long as his or her rulings are in compliance with Islamic law. However, in case a judge is forced to rule by the laws of that non-Muslim country, then it is not legal for him or her to do so and Muslims would not be obligated to abide by his or her rulings. In this case, Muslims would not even be not allowed to appeal to the judge.
As long as a judge passes judgment according to Islamic law, we may not argue that because this judge was appointed by a non-Muslim country, Muslims may not resort to him or her. In this way, Muslims would not have any judge to solve their problems and determine their rights.
Scholars have decided that if Muslims live in a non-Muslim country where there is no Islamic court available and they are in need of arbitration for their rights, then they may arbitrate to a non-Muslim court in order to attain the rights that are rightfully theirs according to the Islamic law. Since it is permissible to arbitrate to a non-Muslim court as long as it is based on justice and gives everyone their right, it logically follows that arbitration to an Islamic judge who is appointed by the non-Muslim government would be permissible to a far greater extent.