Jesus "render unto Caesar" comment was not simply a discourse on the separation of church and state. It was a way of foretelling exactly what was going to happen to Him, in that the same Pharisees who were seeking to entrap him would later have him executed by "rendering him unto Caesar." That is, they would engage in the ultimate act of hubris and hypocrisy by having the Son of God executed, but by turning him over to Pontius Pilate while using their "religion" as an excuse not to do it themselves.
True, but that doesn't take away from its essential truth that there is something obligated to the state (was Paul also reminds us), and there is something obligated to God.
I also find it interesting in the "gold from the fish's mouth" passage where Jesus in essence trivializes taxes, and in essence says, if you walk with Him, the "burdens" of the government will become so irrelevant that it will be like pullilng gold out of a fish's mouth.