Tibet was at times wracked by infighting between rival Buddhist sects. Meanwhile the founder of Burma’s aggressive and expansionistic Konbaung dynasty adopted the moniker of Alaungpaya ( ‘future/embryo Buddha’ ) and, shortly before being blown up by a faulty piece of siege artillery, issued propaganda declaring that his expansionism was just an attempt to make the world more “radiant” for Buddhism.
Of course you can have the same objections that others have raised - namely that religion in these cases were justifications for struggles over territory or resources. But really teasing out religion from other justifications becomes difficult - wars are rarely ( never, probably ) fought for ONE reason. There are usually complex matrices of intersecting human desires and impulses that result in hostility. Ultimately Malthus is correct that people will always find a reason to fight - we seem to be at base a pack-oriented species. We may be able to embrace variable definitions of in-group, but there are always out-groups to strive with.
Even seemingly straightforward religious wars like the expansion of Islam can be teased apart to find different motives. To a significant extent that seems to have been a snowballing affair - the initial trigger drawing the Arabs north were tribal rivalries with Byzantine/Persian Arab clients, many of the new conquerors were barely converted and the immense wealth to be looted a huge incentive. Muhammed arguably favored a universalist faith - his successors initially did not, limiting Islam to a largely untaxed plutocratic ethnic Arab elite. Even the popular notions of Dar al-Harb didn’t appear until 3/4 of a century after Muhammed’s death, post-hoc triumphalist justification for the remarkable Muslim success up to that point ( and the guy who originated the concept ended up dieing in prison ).
So the OP has a problem, because there are probably no religious wars one can point to, that you can’t dig up plausible alternative reasons for. However, that doesn’t mean that religion has no impact and that religious wars in a looser sense don’t exist because they certainly do. I don’t have any problem referring to the early Islamic expansion or the Crusades as “religious wars”, insomuch as they had very strong religious components. Piety really did propel them as a major motive. The only motive, no. But it was justification and an impetus, something that shouldn’t be hand-waved away.
Where to draw the line is tricky. If one side has actual religious doctrine as a primary driving force, I’d be inclined it to label it a religious or at least partly-religious war. So:
1.) Northern Ireland - mostly not. "Catholic"and “Protestant” in this case seem to be in-born tribal identifiers, but the struggle is only brushed by doctrinal differences on the extreme edges. Nutty Ian Paisley could probably be fairly said to have been waging a religious struggle, but he seems to be an outlier.
2.) Founding of Israel - mostly not. Again we have tribal identifiers. The then Christian president of Lebanon had no problem joining other Arab forces in invading the region and many of the Jewish leaders were atheists. For that matter the Syrian Ba’ath were at that time still led by its primary founder Michel Aflaq, a Greek Orthodox Christian by origin.
3.) The Mahdi Uprising - arguably. The primary motivation was anti-colonial, but the Mahdi’s claim of being…well…the Mahdi, was a major impetus to his unifying Sudanese factions.
4.) Thirty Years War - arguably. Like slavery in the American Civil War, religion may not have been the only issue, but it was a major underlying issue from which many of the others stemmed or swirled about.