Happens literally in The Unity Saga as Seven of Nine kills Mara Jade, though at least both parties were established as loving Luke
Hivefled: Nepeta dated and broke up with Karkat before the main story happened, and is horrified at Lereal's suggestion they follow in their ancestors' footsteps by dumping all their other quadrants for each other. Karkat's not best pleased either.
"Living in The Vampire Diaries" has wars over which OC Damon should be with. Some want him with Tori, where the others want him with Sidney (even they're supposed to be Just Friends). The fact Tori is with Stefan while Sidney is single doesn't help, nor does Damon being Sidney's sire
The Arrow story Red has Thea/Roy shippers vs Thea/Sara. One is based in canon with the other having no indication that they even know each other, but has a more BirdsOf a Feather vibe with both being vigilantes.
The Bridge has started seeing this between supporters of the two most popular potential pairings of the fic — Godzilla/Luna and Godzilla/Blade Dancer, the latter having some evidence and the former only being up to interpretation. Hilariously, the author had no intention of any pairings, but has since started dropping hints just because he finds the whole situation amusing.
In-Universe in Paradise Thwarted with the denizens of the Fangirl Layer of Hell. Factions dedicated to different ships spend all their times fighting wars with other factions over whose ship is better.