You seem to have gotten it backwards. "Render unto Caesar" is a passage in Scripture (which the wikipedia article you've linked to mentions), and so it came bef

You seem to have gotten it backwards. "Render unto Caesar" is a passage in Scripture (which the wikipedia article you've linked to mentions), and so it came before the Roman persecution of Christians occurred. From its founding, Christianity made the distinction between secular and religious authority/institution. (There is nothing that says a pope or a bishop cannot also be a king or a prince. They simply have authority in both, analogous perhaps to how one can be a king in one country, and a prince in another, or whatever. But they are two distinct forms of authority, and one is technically subject to the other.) This separation of the institutions of Church and State is indeed only comprehensible in the prior distinction, but separation is, strictly speaking, a heretical notion. Liberalism (which is a Christian heresy) is merely tolerated by the Church, provided it does not encroach on the authority of the Church and the practice of the faith. If that ends, the modus vivendi is violated, and the truce is broken, and war has effectively been declared on the Church. With respect to Islam, it isn't that Muhammad was both a political and a religious leader, but that there is simply no distinction between the two in Islam. That's why it makes no sense to speak of the separation of Mosque and State. The only reason you can distinguish between Church and State is because they're both institutions. A mosque is not an institution. It's just a building used for prayer and such. This distinction between Church and State is utterly foreign to Islam and the rest of the non-Christian world.