The actual question is whether religion had a historic impact on society or whether society had a historic impact on religion. Something neglected in these (sophomoric) discussions is that historically speaking, the separation of church and state is a decidedly modern invention (and a conditionally-adopted one at that). Government and religion both represent a power structure. Piketty pointed out that prior to the French revolution, the Holy Roman Empire owned something ridiculous like 80% of all capital in France, for example. Henry VIII and the Anglican church wasn't about Henry wanting a marriage annulled; it was about Henry VIII demonstrating to the Vatican that Fuck you Clement I'm the goddamn king.

In the end, though, it's a question that isn't even worth investigating. Did a need to convert the savages militarize medieval Europe or did a need to pillage the Holy Land militarize Christendom? Who cares? People died for the justification of a greater cause and that will continue so long as someone makes decisions for someone else as part of any social structure anywhere ever.