Actually, "render unto Caesar..." is Jesus' way of saying we shouldn't care about money. It's not a backhanded attack on anything or anybody. Jesus, as portrayed in the Gospels, didn't employ backhanded attacks. He was pretty straightforward.

That said, I do agree that charity is an individual decision and shouldn't be left to government. But ensuring the common good is part of the role of government, and good people can disagree on how best to accomplish that.