The 'rendering' which the Lord presented had to do with paying taxes. The Lord's words were an answer to a 'seeking' to test His obedience and therefore His righteous conduct..
17 Tell us then, what do You think? Is it lawful to give a poll- tax to Caesar, or not? 18 But Jesus perceived their malice, and said, Why are you testing Me, you hypocrites? 19 Show Me the coin used for the poll- tax. And they brought Him a denarius. 20 And He *said to them, Whose likeness and inscription is this? 21 They *said to Him, Caesars. Then He *said to them, Then render to Caesar the things that are Caesars; and to God the things that are Gods. 22 And hearing this, they were amazed, and leaving Him, they went away. Matthew 22 17-22
What is at the back of the provocation or testing which Jesus suffered may have been simply a religious spirit of hypocrisy. A kind of reverse trap. A little like saying:
"we know you are a man of God because of the things you do, but the pharisees and all truly religious men despise the dominion of Caesar over Israel. So should we submit to Caesar?" "Should we meet his tax demands? Is it lawful?
It clearly was Caesar's law. So what is this 'other law?' The spirit of the question is hypocrisy, but the snare was in seeking to bring the Lord into rebellion. Hence the answer of the Lord, "show me who's head is on the coin," settled the issue.
There is another verse which seems to carry the same root of meaning. "If a man demands your coat, give him your shirt also." Who but a man in authority could demand your coat. If he does "give him your shirt also". In other words submit to all in authority.
For me this principle is the most difficult thing in the world. How easy it is to resist and thereby come into condemnation. Paul said "I hear of your good conduct, in that you rejoice in the taking of your homes". The sermon on the mount carries in parts a similar meaning.
None of this however has anything to do with being part of the state as far as these verses teach. Voting, or involving oneself in politics, encouraging others to do the same, may end up with that one, and ultimately those who follow the injunction, being found an accomplice in perceived unrighteousness, and with it a bearing of ill effects.
Here in the UK it is already a criminal offence to speak against homosexual relations, let alone perverse lawful union. Not a direct law, but "the preaching of hate". Where then for those who now live in the UK and love the Lord does wisdom lie. The separation between state and church is the body of Christ crucified for sin. In this world we cannot possibly resist or avoid the state. We can however lay hold of our part in Christ's death and thereby render unto Caesar that which is Caesar's without involvement in politics. The time is now at hand in the USA for a reaping of this same principle. These laws will be passed and when they are they will bring with them a hatred of christians hither too unseen in the USA.
In the end it will be an unavoidable reality of life that some in Christ at least, being equipped by God for that purpose, will have to preach the truth concerning a man's conduct and its consequences before God. This will mean "suffering for the sake of righteousness" and not suffering ill effects by involvement in politics. I truly believe with a growing sadness and concern that saints in the USA have already laid the foundations for this terrible effect. It is the Constitution of the United States of America.
Andrew