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(My opinion is that neither should be used, but a majority of Americans disagree with me).
To be pedantic, crusade means "holy war" and jihad means "to struggle", so jihad should be more acceptable than crusade, but in English, jihad essentially only has the holy war meaning.
Fun fact 2: what happens after The Butlerian Jihad? Return of the empire!
Abomination!
I have known Indian / SE asian Ice cream shops named Hitler.