1) Your episode must be something that could have appeared on TNG when it originally aired (think 1990s TV).
OK, so a DS9 ep that could have appeared on TNG. That probably would make it fairly generic Trek, right?
"Sworn Enemies"
Two of the more orthodox Bajoran denominations decide to have it out on the station, before the eyes of the Emissary. Their main point of contention is whether the 37th Prophecy of Onteiga Las, made some 12 millennia ago about the Appearance of the Orbs should only be interpreted literally, or both literally and metaphorically. However, even the Emissary cannot calm them down or get them to talk, and when Kai Winn tries to intervene, she's taken hostage by the 'literal' party to put pressure on the Emissary to decide in their favor.
It takes the combo of Kira and Tekeny Ghemor to convince them that reconciliation between 'sworn enemies' is possible.
But even then, splinter factions secede from both groups that still don't want to reconcile. Ironically enough, they find one another in their assessment that 'the Cardassians never were true enemies in the first place; they only could waste our bodies, not our paghs, the way heresies can'.
Next episode: Torps and Orbs.