Some people say Sharia is nothing to worry about, but that's a nonsense. Read the "Reliance of the Traveller", the classic manual of Islamic jurisprudence. Others say, well in any case, it's not in our legal systems, so there's nothing to worry about. But that's also a nonsense. In the UK there are 87 Sharia courts and in the US regular attempts to have Sharia accepted in the courts.
Another apologia is that, "well, it's no different to the Jews using their own laws for mediation". Well, that too, is a nonsense:
Contrary to the popular misapprehension, sharia is not like halachah and sharia courts are not like the batei din [Beth din]. Jews believe that the law of the land is the law. Decisions of the batei din are therefore essentially informal rulings; any binding decisions about family or other matters are made in accordance with the law of the land, which is acknowledged to hold sway.
Read more here.
Another apologia is that, "well, it's no different to the Jews using their own laws for mediation". Well, that too, is a nonsense:
Contrary to the popular misapprehension, sharia is not like halachah and sharia courts are not like the batei din [Beth din]. Jews believe that the law of the land is the law. Decisions of the batei din are therefore essentially informal rulings; any binding decisions about family or other matters are made in accordance with the law of the land, which is acknowledged to hold sway.
Read more here.