"Power tends to corrupt, and absolute power corrupts absolutely. Great men are almost always bad men." (Emerich Edward Dalberg Action, 1834-1902)
Jesus said, "...render to Caesar the things that are Caesar’s; and to God the things that are God’s," (Matt. 22:21). Caesar represented the government of the time and Jesus was telling Christians to display integrity when dealing with the government in which they live. The immediate context dealt with taxation and Jesus did not deny the government's right to tax.
Paul said, "Let every person be in subjection to the governing authorities. For there is no authority except from God, and those which exist are established by God," (Rom. 13:1).
In Acts 5, the Apostles were arrested and imprisoned (Acts 5:18) for preaching and healing in the name of Jesus. An angel of the Lord freed them (5:19) where they again began to teach. They were then brought to the Council (5:26-27) and told not to teach in the name of Jesus (5:28). But, Peter and the Apostles responded to them and said, "We must obey God rather than men (Acts 5:29)."
So, we are to be subject to the Government according to Jesus and Paul and yet we are not to be subject to them when they contradict God's word. This is the problem with people running governments. When they get into power they tend to corrupt things.
When any government acts in a manner that contradicts the Bible, then Christians are to follow the Bible and not the government's proclamations. For example, the United States has legalized abortion. But, the Bible says do not murder (). Therefore, Christians are not to have abortions. The U.S. is favoring homosexuality as a legal standing with marriage rights. But, the Bible speaks against homosexuality. Therefore, Christians are not to support of homosexual marriages and unions.