When Peter came into the house, Jesus was the first to speak. “What do you think, Simon?” he asked. “From whom do the kings of the earth collect duty and taxes—from their own sons or from others?” 26“From others,” Peter answered.
“Then the sons are exempt,” Jesus said to him.
Christ told us that we are exempt.
Caesar was collecting from foreigners whom were the Jews.
So saying "render unto Caesar's what is Caesar's...." does not apply.
The Jews in Israel were foreigners to Caesar.
So the question remains without justification. When the Orthodox pays taxes and it funds wars and misc other things that are not Christian is it "sinful", seeing that we are exempt.
You are missing the point horribly. For one, here is the full story:
24And when they were come to Capernaum, they that received tribute money came to Peter, and said, Doth not your master pay tribute?
25He saith, Yes. And when he was come into the house, Jesus prevented him, saying, What thinkest thou, Simon? of whom do the kings of the earth take custom or tribute? of their own children, or of strangers?
26Peter saith unto him, Of strangers. Jesus saith unto him, Then are the children free.
27Notwithstanding, lest we should offend them, go thou to the sea, and cast an hook, and take up the fish that first cometh up; and when thou hast opened his mouth, thou shalt find a piece of money: that take, and give unto them for me and thee.
Then there is also the fact that our Lord and Saviour was pointing out an historical fact. Romans and the inhabitants of Italy were exempt from taxes.