Hitler had many priests and bishops willingly collaborating with him. And the Nazi regime strengthen the power of the Catholic church.
Yes, some priests opposed him and were beaten and killed. But that was the exception.
You might not consider the nazi views were religious, but that does not matter, because the catholic church of the time, thought it was. And that is why, even in defeat, the Catholic church and the red cross, assisted the nazi regime.
And your idea that religion does not cause war is completely wrong. At least 25% of all wars in human history, have a direct religious cause.
FFS, all you have to do is look at the Crusades. Or the 30 year war. Or the Muslim conquests. Or the Rwandan genocide. And so many conflicts in human history.
Even in the case of many wars that had political or economic reasons, religions still played a part, even if it was just to convince the populace to fight.