You are going to find a difference of opinion as to who is truly Christian.
You are going to find a difference of opinion on the question as to what is Caesar's.
Only among those who are not truly Christian or at that time following the Law.
Actually I ain't. Well people may disagree with my point, but they are wrong. This ain't "opinion time. It's basic Judeo-Christianity.
You have to look at the rhetoric of Christ throughout most of the synoptics especially within Mark. There is irony, oft in the form of the Socratic variety with a "true" cynical turn (please google what cynicism means before arguing).
He constantly answers questions with questions that leave the accusers in a lurch. If they answer what is in their hearts they will be found to hypocrites or put into the very same danger they would like put Christ.
Here they are trying to get Christ to speak again the tax.
People jump the gun and think Christ's answer is about paying taxes per se, but it ain't.
What does Christ ask them / tell them?
Render unto Caesar what is Caesar's and unto God what is God's.
Now the implied question?
Not what is Caesar's per se,
What is God's?
This is basic Judaism come Christianity 101.
How do you answer?
Nothing belongs to you, not even your own life. All is God's. End of discussion. What is given to you is for you to steward to the glory of God to the degree you can.
Tithing, Temple Sacrifice, etc. are ways of acknowledging this basic tenet of Judeo-Christianity, which seems to pretty much go missing anymore.
Whether you pay the tax is it a matter of proper stewardship of what you were given by God to His glory. There is no easy answer here.
Sometimes taxes may serve the Glory of God, as well as military service, etc.
But this has ABSOLUTELY nothing to do with some division between worldly offerings and "obedience" to governments versus some spiritual offering to God.
That is gnosticism for real. The notion that what is God's ends with the dirty complications of commerce and government and the like. As long as we are good citizens and go to the Divine Liturgy, we are doing what Jesus suggested here.
Everything is God's and all is given to us by God, even Caesar and his tax. How we handle and steward what we were given obviously can get very complicated.
But if a "Christian" or a "Jew" does not believe that everything is God's. Then they ain't no proper Christian nor Jew.
Even my backwoods Baptist, three-fingered preacher knew that much. I would think the Orthodox and Roman Catholics would know as much as well.
What we render to Caesar is what is God's in light of proper stewardship of what were given.
Caesar's life doesn't belong to him, much less that coin with his image and name on it.