What influence and impact does Islam have on social structures / governments / societies?

I understand that for Muslims, every verse of the Quran and every hadith of the prophet must be followed to the letter. From what to say before going out in the street, how to dress or what is the form of government. Every element of private and public life is regulated, and hence the social organization of Muslims is diametrically opposed to that of a democratic state. The Quran is immovable, and it establishes a whole series of clear rules, while Christianity is much more diffuse and “relative” in my point of view. What real influence does Islam have on social structures, governments and societies?