I would suggest exploring the nuance surrounding the "render unto Caesar" passage. Remember, the Pharisees wanted to discredit Jesus. If He said, "Jews owe taxes to Rome," He would discredit Himself. If He said, "Do not pay taxes to Rome," He would have been crucified, or at least imprisoned, then and there. It was a lose-lose trick question. Instead, He asked for a coin.
Why would the Pharisees have a Roman denarius issued primarily to pay Roman soldiers and officials?
What was the image and inscription on it, beyond just the face of the emperor?
What is really Caesar's, especially in context of Jewish people familiar with the Psalms, the law, and the prophets?
There was a reason the crowd was amazed. He elegantly disarmed their trap in a way they could not counter.
We are commanded to live at peace with the world so far as is possible for us, but neither this passage nor Romans 13 really confers legitimacy on man's governments.