I would think that not supporting the lesser evil is the strongest response we can give.
Jesus is my King, my President, my Prime Minister - to support any who go against Him is foolishness.
When I read the gospels Jesus was very involved in what was going on, He condemned the religious leaders and He condemned the corrupt leaders including the Romans.
People think that when He said "render unto Caesar that which belongs to Caesar" that He was saying that He has nothing to do with human government. But that is a complete misunderstanding. He said "give unto God that which belongs to God" which referred to the things that have the image and superscription of God on them, ie man.
People are naive, they think the worldly system is happy to have a "separation of church and state" principle, that this false. The world wants to control you lock, stock and barrel. They want to make you a slave and Jesus said no, the people belong to God, you can keep these Roman coins. They were asking if they should pay tax or not and He was saying it won't matter once all the people are worshipping God the money and the entire system will go up in flames.
The world is fighting the battle from the flesh inward to the heart, and Jesus is fighting the battle from the heart outwards. Both Satan and the Lord desire to be Lord of All. Caesar and all human government is simply usurping the Lord's position.