One aspect of Muslim culture that runs against the grain of Americans is the
Theocracy is indeed one of the most dangerous political phenomena the world faces today--especially Muslim, Christian, and Jewish theocracy. That having been said, what the Koran says or doesn't say isn't terribly important. Believers of all three of the Abrahamic religions commonly ignore or explain away elements of their Scriptures that contradict the norms of civil society. Ambrose Bierce famously defined a Christian as someone who adheres to the teachings of Christ to the extent they are not inconsistent with a life of sin. I think that's true of most believers. Having said that, there are plenty in all three religions who wish to import religious dogma into the business of government, and you are right to resist that. On the other hand, there may be special cases where civil law grants certain exemptions or latitude to deep matters of conscience. For example, US law grants conscientious objectors exemption from military service for reasons of religious conviction. Accommodations are often made in civil institutions of government like prisons for dietary restrictions--pork for Jews and Muslims, for example. Civil government often suspends is operations on religious holidays.
The philosophical problem with setting a religious basis to public policy and law in a pluralistic society is that religion appeals to reasons not available and not acceptable to non-believers. Moreover, in maintaining that they have apprehended absolute truths, religions commonly regard their opponents as absolutely wrong. Even worse, the religious not only regard those who disagree with or defy them as not only absolutely wrong but also as dangerous in the most profound way--threatening to lead believers not only into error but also into eternal damnation. As a result infidels, heretics, and dissenters warrant for believers the most extreme censure and punishment. Of course, it's by no means true that all or even most believers follow out the logic of their religions in this way. And it's important not to conclude that Christians, Muslims, and Jews present widespread threats to society. The hard work of civilization has thankfully made religion largely safe for civil society. Keeping it safe however t does require continued labor.