religious war
A war primarily motivated by religious differences or goals.
ヨーロッパでは宗教戦争が何度も起こった。
Religious wars broke out many times in Europe.
宗教戦争 is the neutral, factual term for a war fought between religions, while 聖戦 carries a more rhetorical or ideological tone of righteous, divinely-sanctioned struggle.
Compound of 宗教 (religion) and 戦争 (war).