There would only be civil cases where all parties have agreed to go to this court.
No different from mediation.
If they wish, two parties can agree to have a civil dispute decided by the man in the Mickey Mouse costume at Disneyworld .
I would agree if this person had not stated that Sharia is above US law.
If it is a moral or religious matter...who cares? But it doesn’t appear to be the case.
Post 152 for my take on that.