Lol @skyeaterairplane: Communists are godless, as in they don't believe in any sort of God. They believe in a "perfect man" achieved through worldwide socialism and the advances that they think would be brought by that. Marx and Lenin both did not believe in a God, and Lenin actually replaced a Russian Orthodox based monarchy. Note that communists are on the far left of the political spectrum, which is commonly (and incorrectly) referred to the godless side. The term you're looking for is something like a theocracy, where a nation-state is ruled by religious leaders, priest-kings, etc. An example would be Egypt with the Pharaohs.
On an actual song related basis: I really did enjoy this song, I knew they were Christian from the first time I heard them (kinda impossible to ignore those lyrics), but that's not why I like them. It just adds a little to it. =)