Keeping in mind the Jewish code was and looking at Israel, remains essentially tribal. The in group and everyone else.

With Christianity, it was the emerging Roman Empire adopting it as a way to provide a code across the Empire. Essentially the first globalization.

With Islam, it was the realization that an intertribal code/creed gave them more power, larger group. So the creed came before the state, as opposed to Christianity, where the creed was adopted by one state.

Which is why the civil and cultural relations differ. "Church and state" are not as separate as we might think.