You can't deny that religion didn't play an important part in it or that religious zealots aren't more prone to violence or being easily manipulated by opportunist psychopaths, which btw partly explains while the Middle Ages fucking sucked.
Eh, religion was such an ingrained part of all human life it seems very reductive to try and pin it as the primary mover in the shit show that was all of human history let alone the middle ages. If you look at say, the Mongol invasions, responsible for arguably the biggest loss of life due to war in that entire era, religion was if anything, a tiny part of a murderous whole. The Khans were not religious by any real modern sense of the word, and they slaughtered tens of millions.
Humans all have that part of their mind where faith is the primary motivating factor. As religion becomes less and less popular, we're seeing political ideology pick up the slack. I mean look at Maoist China, or modern North Korea and tell me those weren't religious.