The Roman coin was stamped in the image of Caesar and Jesus says it is OK to give it back to Caesar. Then he says give to God that which is God's. So the question is: What is stamped or made in the image of God?
Answer: Man
For Gen 1:26 states And God said, Let us make man in our image, after our likeness.
So it seems we have to give ourselves back to God.
Therefore render to Caesar the things that are Caesars, and to God the things that are Gods.
But what if Caeser is a total, liberal/socialist idiot???