Caesar claimed to be a God. This is a violation of the Jews' 1st commandment. His image on the coin was a graven image--a violation of the Jews' 2nd commandment. So what part of "Give a false god what he has coming to him" are you confused about?
Unto Ceasar I hold accountable all who Violate Ceasar's laws. Unless and until they come into conflict with God's laws.
It was these conflicts of the imperial Roman occupiers' laws with Jesus' Golden Rule that is the main theme of the gospels' account of the life of Jesus!
Loving your neighbor as Jesus commanded us to, has nothing at all to do with Man's physical Law.
As you pointed out above, it has everything to do with it when there is a conflict. Just as the operators of the Underground Railroad were not bound to tell the U.S. Fugitive Slave marshalls where the escaped slaves were hiding, Clinton was not bound to incriminate himself in front of the sex police (even if he had pushed for the draconian laws himself a few years earlier--just as Rush is not bound to obey the unconstitutional drug laws that he pushed for years earlier).
Nice to see you this afternoon, Mr. Carville!