The Roman Empire provided the religious basis for just about every political group in Europe up until the french revolution (ww1 really). Why do you think every king had a divine right to be king? Because ultimately they were the descendants of Christian Rome, or kings who bent the knee to rome and turned to accept christianity. Czar literally means caesar and the entire orthodox church is derived from byzantium. Rome was (and still is) the center of the christian world.
You radically underplay the role of religion in human history. I think its all made up stories that wither under the scrutiny of a clever 5 year old, and I'm sure you do too. But for most of human history people simply didn't know better, and religion guided their life. It was absolutely inseparable from politics. To suggest they would be separated would be like saying you can separate morality and politics today. Religious fanatics haven't ruled the world for the vast majority of human kind by accident. No doubt many didn't believe it, and no doubt many had completely non-religious priorities, but they still had to pretend. Even today the president has to pretend to be religious, just as I'm sure a few psychopaths pretend to be religious so they can shoot a bazooka or get a wife in Syria.
I'm a bit disheartened by how naive you seem to be about this. We live in a liberal educated wealthy democracy and religion still dominates politics. A bunch of 3rd century peasants certainly knew no better, and it was the easiest way you could trick them into fighting for you. The ones to clever to fall for that, you kill or bribe. You call it politics but it always has a religious angle and overtone to it. Was Stannis fighting a religious war or a political one?