The Constitution and the Muslim Faith

I don't know enough to make blanket statements, but I want to think through a tension I see between a constitutional form of government and any faith that cannot subordinate itself to civil law.

Our founders built a country that forbade religious persecution and elevated an agnostic body of law to supreme status, guaranteeing individual rights that no religious or political dogma could abridge. The Constitution became, in effect, our political arbiter. My question is whether any religion that cannot subjugate itself to that framework can fully coexist with it.

(This is a 2009 reflection of mine, written as an open question rather than a settled conclusion.)