In the Gospel the Pharisees ask Jesus whether it’s lawful to pay taxes to the Roman Emperor. They hope he will say "No" so that he gets in trouble with the Romans.
But Jesus doesn’t answer the question directly. He changes the angle of the conversation.
Jesus asks for a coin, points to the picture of the Emperor on it, and says give to the Emperor what is the Emperor’s and give to God what is God’s.
Jesus is recommending not absolute but qualified loyalty. That is to say, if a government provides needed goods and services then we must, in justice, give back to the government our loyalty and support. To use this passage as a justification of unconditional loyalty and support of corrupt and totalitarian governments in a misunderstanding of what Jesus is teaching.
Christians must together discern whether and to what extent a given government and its policies merit their loyalty and support. But total and absolute loyalty and service is a debt that we owe to God and to God alone.
How do we pay what we owe God? By loving others, using our gifts and abilities for the glory of his name and, in every way, living in a manner worthy of the reign of God.