I think your definition and perspective are way off. First and foremost, I'm not sure where you're getting your definition from but anarchism has never been defined as a "state of disorder due to absence or nonrecognition of authority". Sounds like you're relying on TV to define words for you. A simple Merriam-Webster search would have shown you that anarchism is defined as "a political theory holding all forms of governmental authority to be unnecessary and undesirable and advocating a society based on voluntary cooperation and free association of individuals and groups". There's nothing in that definition about not having rules and there's nothing in that definition about not having God as your authority. I think most anarchists that you talk to would agree that there is nothing wrong with having an authority over you as long as that is agreed to voluntarily and not by force. Even an amateur could read the NT and determine that Jesus was no fan of earthly governmental authority. Did he believe in the authority of God? Absolutely. But I believe is a stretch to say he believed in the authority of men. What the NT says he did, he did voluntarily for man.
Secondly, I do not know of any Christian Anarchists, these "Carnal Christians" as you refer to them, who believe they should "help God by trying to bring his Kingdom to replace this fallacious system". Every one of them that I know of simply wants a society based on peace, free association and voluntary exchange without government force and interference. They aren't trying to help God do anything. They're just trying to have a peaceful existence with the rest of humanity until His kingdom comes.
I'm not a Christian but I would much rather live in a world full of Christians, Jews, Muslims, Hindus, Buddhists etc. who believe this way than what we have had up until this point. More death and destruction has happened under earthly rulers acting falsely "in the name of God" than anything else. Isn't it high time we kick the earthly rulers to the side and let mankind live and interact with each other peacefully and voluntarily without the use of force?