Again I say, "Pay your taxes, just don't expect them to do any good." Which is what I think Jesus was saying. We pay our taxes because it is strategic.
We are not to fight for political victory, but for the victory which transcend politics. We are to demonstrate the emptiness of political achievements by achieving more outside of and despite the political process.
Does the state promise you bread and circuses? Demonstrate the emptiness of that promise by providing the bread of life and the adventure of discipleship.
Does the state promise protection from foreign enemies. Demonstrate the emptiness of that promise by loving your enemies and praying for them, settling peacefully with them when possible, and winning your brother over.
Does the state promise welfare for the poor? Demonstrate the emptiness of that promise by giving sacrificially and voluntarily and helping to restore dignity for invalids by providing them a way to serve.
Does the state promise an education? Demonstrate the emptiness of that promise by educating yourself and behaving as the Bereans did. Challenge your mind and ask difficult questions of yourself and others. Work out your own salvation.
Pay your taxes. Then ignore the existence of the state, and behave like a citizen of heaven.