Should non-Muslims be subject to Sharia law...??? No. I do not think non-Muslims should be subject to Sharia law. This is because we all have the right to select which law and rules we want to obey. The sharia law cannot be imposed on anyone without the person him/herself committing to the laws and obeying them. Everyone is born free and we therefore have the right to select what religion or set of rules we want to follow. Some of the people might have not even heard of this law and would disagree with its rules. Therefore, non-Muslims should not be subject to the Sharia law.