Do they do arbitration? Not exactly:
Breitbart Texas spoke with one of the “judges,” Dr. Taher El-badawi. He said the tribunal operates under Sharia law as a form of “non-binding dispute resolution.” El-badawi said their organization is “a tribunal, not arbitration.” A tribunal is defined by Meriam-Webster’s Dictionary as “a court or forum of justice.” The four Islamic attorneys call themselves “judges” not “arbitrators.”
El-badawi said the tribunal follows Sharia law to resolve civil disputes in family and business matters.
What happens when there is a conflict between sharia law and Texas law? They go with sharia.
http://rightwingnews.com/immigration/sharia-law-texas/
Thats right, second reading of your post, you are correct.
Arbitration is considered to be legally binding. This is presented as non binding dispute resolution, which fills an intermediate area between mediation and arbitration.
Oh, to add, there’s actually something called an “arbitral tribunal”.
So the key term here is still “non binding dispute resolution”, with terms like tribunal or arbitration being contrasted based largely on semantics and preferences.
Regarding the part about Sharia always superceding TX law. That’s flat out wrong and opens them up to prosecution. They are certainly welcome to challenge it, all the way up to the Supreme Court. They may win on some lower level things (under the 1st Amendment) but certainly not on things like divorce, domestic abuse or honor killings.