"That just isn't the case, The Great War, World War II, Korean War, Vietnam War, Falklands.... Even with conflicts where the antagonists have different religions, it generally isn't religion as such that's at issue."

First of all the idea that there is a Great War is risible. There was nothing great about World War II. War is never "Great". The message that's not received here is that both the Korean War and the Vietnam War were championed by Christian anti-Communist groups and much of the fighting was done by those who had religious indoctrination that allowed them to participate and justify the killing of people who believed differently from them. Vietnam or Korea offered no legitimate threat to the U.S. To say otherwise is bogus. The evidence is that this is still being done in Iraq, Afghanistan, Yemen, and Islamic countries because the Crusades are still going on and the American Military is indoctrinating more recruits toward its Christianity.

World War II might be a slightly different case but remember that Hitler, who was raised a Catholic, used the inherent religious discrimination against Judaism, which is a religious precept. Hitler allowed Catholicism and Lutheranism to flourish during his abominable reign. The "Kirches" were active and involved in subjugating Jews and this points to the role of religion here.

As to the Falklands, the Brits have a Protestant base which may have influenced their incursion into a Catholic country.

There is a religious aspect to these many wars. It is the case.