Answer:
Step-by-step explanation:
No!
Church and state should be kept separate. Modern Warfare with few exceptions, is not fought over religious differences. Usually the root of the problem is economic. The second world war was not really about the Jewish Question, or Jewish relocation, although Germany used it. It also wasn't about the power of Pope Pius X11. The Vatican employs a very small swiss guard to protect the Pope.
England and Germany were both Protestant.
Poland was Catholic
France was/is Catholic.
Italy was/is Catholic.
Russia at the time was not Catholic, but it wasn't Protestant either.
Greece was Catholic
Turkey was neither. (Muslim).
Palestine Jewish.
Egypt Muslim.
Much of North Africa was Muslim
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Even though these are major religions, they have little to do with how battles were fought and how alliances were determined.
Your question is not about the alliances. Your question is should they? I think a better question is Can They?
My own opinion is no. Religious wars are nasty things. We should avoid them.