Let's put 'Christian anarchists' aside for now since I think we more wish to argue with regular old God-hating anarchists/punks/activists/leftists. The message we need to deliver to these people is this: capitalism, democracy, or whatever is not the right enemy. Sin is.
People concerned primarily with social justice often completely lack personal justice. Activists I know are not only the most sexually immoral people I have ever met, they are also the most, disloyal, lying, stealing and cheating. They have elevated their feeling of oughtness about social justice to the point where it had drowned out their feeling of outness (otherwise known as a conscience) in their personal lives. You cannot escape Genesis Three.