Those unfamiliar with the biblical world frequently turn to today's gospel pericope to argue for two distinct realms in the world. One, the church, belongs to God; the other, the state, belongs to us humans. Neither should interfere nor cross over into the other. Nothing could be further from biblical faith.
Jesus' confrontation with his enemies is resolved by having recourse to basic first century Middle-East economics: who owns the country's money? In contrast to modern monetary practice, the country's leader was looked upon as actually owning the currency circulating in his or her realm. In this case, if some of the coins circulating in Palestine are Roman denarii, the Roman emperor is their owner.
So when the Herodians - who work for the occupying Romans - and the Pharisees - who despise the Romans - jointly ask Jesus about the legality of paying taxes to Rome, Jesus points out the obvious. The image and inscription on the coin are a sign of Caesar's ownership. If Caesar wants his money back in taxes, one is obligated to return it. Neither the Herodians of Pharisees can argue the point.
The problem arises when Jesus ends his words with the command, "... and repay to God what belongs to God." Some contend that at this point Jesus is dividing the world into Caesar's realm and God's realm, and as I mentioned above, there should be no overlapping.
More than 500 years before Jesus' birth, Deutero-Isaiah turns heads and shakes theological pillars by referring to the Persian emperor Cyrus as "Yahweh's anointed," (The Hebrew word for anointed is "Messiah" - "Christ" in Greek. In other words, the prophet's calling him "Cyrus the Christ!")
The prophet constantly promises his fellow-exiled Jews in Babylon that Yahweh will soon return them to the Promised Land. Though they're glad to hear his message, most are disturbed by the details of their return. Counter to expectations, this new Exodus will be led not by a righteous, Torah-abiding, circumcised Jew, but by an uncircumcised, Gentile pagan! Why couldn't a good Jewish boy be the new Moses?
Well-informed about international events, Deutero-Isaiah knows Cyrus is conquering one country after another. And wherever this Persian leader goes, he grants the conquered people freedom to practice their own religion, to worship their own gods. The prophet's convinced that when Cyrus finally gets to Babylon, the exiled Jews will simply inform him that, to practice their faith and worship their God, they must return to Jerusalem and rebuild the temple. With a few modifications, that's exactly what happened. But many scholars believe that before it happened, Deutero-Isaiah was killed by his own people for teaching that Yahweh's anointed would be Cyrus. His ability to see God working through all wasn't shared by all. Deutero-Isaiah would have been the last person in Babylon to have pushed for a gulf between temple and state.
In a parallel way, Paul begins the earliest Christian writing we possess - 1 Thessalonians - by reminding his young Christian community, "Our gospel did not come to you in word alone, but also in power and in the Holy Spirit and with much conviction." In what does his "gospel" consist? We presume it's the same as Jesus' "good news," that God is present, working effectively in every aspect of our lives. It's the basic formulation of Jesus' faith.
So when Jesus says, "Repay to God what belongs to God!" he's presuming everything belongs to God; not just the coin, but the Herodians, the Pharisees, and even Caesar. God works through everyone and everything. That belief still disturbs many "good folk" today. But even John Courtney Murray, who doggedly fought for separation of church and state, still presumed God was working in both the church and the state.