Greetings,
Thanks to Wikipedia for this image. It's the Roman Denarius, probably the subject of the "render unto Caesar" debate. The inscription reads “Ti[berivs] Caesar Divi Avg[vsti] F[ilivs] Avgvstvs” (“Caesar Augustus Tiberius, son of the Divine Augustus”), claiming that Augustus was a god, and Tiberius the 'son of God'.
That's part of the reason why Jesus' answer confounded the Herodians and Pharisees in their hypocrisy. He's asking, who are you serving, the One True God, or this Roman pretender to the throne?
The incident in Matthew 17, I think, is the temple tax. Here, Jesus is saying "my disciples owe their allegiance to one greater than the temple."
One thing we always find in Jesus is that He had perfect answers. Sometimes we see only one angle but on examination, His answers and teaching were addressing more than one type of audience and even today, the many different peoples throughout the world can and do see truth in His words. (I am reminded here that He is the Truth as well as the Word)
As Hekuran pointed out with the picture he provided for us, the Herodians would have been somewhat baffled and left speechless, particularly against Jesus and His disciples. Render unto God what is God's would appear to be an agreement or acknowledgement regarding the way the Herodians viewed their gods and the use of inscriptions on coins to express their thoughts. Therefore they are totally disarmed should anyone try to suggest that Jesus was being dissident in His teaching regarding money and the taxes. Likewise, to render unto Caesar what is Caesar's would imply that the words and teaching He gave were in no way opposing the rule of Caesar. On the contrary and additionally, the answer Jesus gave would have appealed to their way of thinking and reasoning - relativism.
But for His disciples and for us, too, the words He spoke concerning the children being exempt from taxes implied that as heirs to the Kingdom, which is not of this world, render to give unto God what is God's as to mean that we give our allegiance to God, our Father and are fully exempt from doing as the citizens of this world do, nonetheless, in order to not have accusations against the Gospel, we ought pay taxes as requested. If you live in a country and use its money then it is only fitting to abide by the rules of its use.
Some may suggest that Jesus was avoiding any action against Himself, but that needs to be in context of the will of His father, namely that for Jesus to be totally free of any accusation brought against Him, that no man nor satan could accuse Him of any valid wrong. Jesus backed up His teaching to the Disciples and to those who would follow with the miracle of the coin in the fishes mouth.
Surely Jesus could have said He wasn't paying and given reason and been prosecuted for it and like Daniel and his friends come out of the fire alive so the thought of fear of dying or attempted execution or the like would not be an issue to Him. Instead we see an entirely pure reason for His answer, not only preventing His death from happening before the appointed time, and as said, that He would remain blameless (which is the only way He could effect being the propitiation for our sins, the exchange for us, a spotless lamb) while also keeping His Disciples safe from premature persecution and being dragged before the authorities.
He was also teaching His Disciples the reality and truth of who they were and who those would follow Him would also become. Throughout the Gospels we witness the ongoing instruction He gave His Disciples, teaching them about the new relationship of the new testament and covenant of God.
To the Jews, the Pharisee and Sadducee and High Priests and Scribes and Lawyers (instructors in the Law of Moses) and even the Levite, He offered no reason for blasphemy nor insult against the Law leaving no room for any accusation from them or the decreasing Law which Jesus was obliged to keep and follow as a Jew. (again we see also a protection of His Disciples here)
Christ was not teaching revolt and anti authority mindsets. His message was and is the Gospel of the Kingdom, which brings Life to those who hear it, regardless of who they are or where they are. It has nothing to do with anarchy nor dissension. It is an invitation to enter in... to be in the world but not of it; to become citizens (fellow citizens) with the saints in the kingdom of God and heirs of the promise of Salvation. The Apostles taught likewise.
As children (except ye become as children ye can not enter the Kingdom of God) we certainly don't have to pay our Father any taxes!
Let the world do as it will. We who believe belong to the Lord and seek to do His will, only.
Bless you ....><>