Conservatives in the west, particularly in America, are terrified of what they call “Sharia creep,” that is the legal undermining of historic western democracy with the law-code based in the Islamic holy text, the Qur’an.
Here is what the Qur’an requires (in an excellent piece you should read):
Regardless of this nostalgia, the thought of living under any rules remotely “Islamic” repulses Westerners. Take comfort in that 99.99% of immigrant Muslims have no motivation to overthrow Western democracies. It is these republics that uphold Quranic principles such as freedom of religion and expression (2:256), equality before the law (4:135), presumption of innocence (49:6), gender equity (4:32, 33:35), social safety nets (9:60), rule of law (33:60), and strong ethics (70:21-70:33).