I think ancient history and modern day events disprove this statement....in fact, fanatical religiosity is probably the biggest cause of death the world has ever known, other than disease and famine, etc.
I understand your point that killers will kill no matter what, but institutionalized belief systems, be they religious or political, can be used to indoctrinate, brainwash, and turn otherwise peaceful people into butchers.
There were warring states, and families, before organized religions existed. Not saying religions aren't used for violence, they can be, just that if you're talking about ancient history, states are far more ancient, and bloodthirsty, than organized religion.
Yup, that's why I included political beliefs in there