QCA is a method of causal data analysis. If your research question involves cause-effect relations, and if you think that QCA's underlying INUS theory of causation reflects these relations, then QCA is surely an option for you.
Islamic (interest-free) banking is even more regulated than conventional banking, because except regulator in Islamic banking there are Shari'ah boards (or Shari'ah supervisory boards), which regulate Islamic banks' business (e.g. conduct monitoring, approve contracts and new bank products and control their application, take care about Shari'ah law implementation in all bank business activities, etc.).