Back in its heyday, Pirates of the Caribbean fandom was split into approximately three groups: the people who wanted Will/Elizabeth (Willabeth) to happen, the people who wanted Jack/Elizabeth (Sparrabeth) to happen, and the tiny group who completely stayed out of it and just watched the madness, usually complete with pointing and laughing. On one forum, these "debates" got to be so bad that the administrators completely shut down all "shipping debates", and had to relegate the respective shippers to their own discussion threads
And it wasn't just that forum either... fans on a certain website's message board did it too. To extreme levels. There was a point where there was nothing on said forum but shipping "team" threads, and bashing of X character.
And when you add in the Ho Yay shippers, things just go nuts. Team Jack/Will and Team Sparrington are the major players here; the latter often aligned itself with Willabeth shippers, while the former just wanted Elizabeth to die horribly. Then there's Team Sparbossa, which started becoming more popular after Barbossa returned in a slightly less villainous role from the 3rd movie onwards...
Not even Pixar is safe anymore. Ever since Toy Story 3 came out and the amount of Buzz/Jessie shippers increased tenfold, shipping "debates" have sprang up. More extreme Woody/Jessie shippers defend their side till the end, some seemingly convinced that Pixar is intentionally toying with them (no Pun intended). Still, Buzz/Jessie shippers aren't innocent either, as some will jump on any Woody/Jessie piece and decry it non-canon. Then you bring Buzz/Woody into the mix...no wonder people like the idea of a Toy StoryOT3 so much.
Avengers: Infinity War saw the rise of Tony/Stephen shippers who quickly formed a rivalry with the Steve/Tony fans. It doesn't help that many of the Tony/Stephen shippers are former Steve/Tony shippers who are upset with the way Tony was treated in Civil War.
Since its release, Frozen has sparked a rabid shipping fanbase, largely due to Elsa's status as Launcher of a Thousand Ships, the film's limited establishment of canon relationships, the popularity of crossover shipping and the integration of the film into the already chaotic Rise of the Brave Tangled Dragons fandom, and the fact that the film's main cast is fairly small, and thusly, non-crossover ships tend to take on a controversial nature (ask any fan of Elsanna, Helsa or Hanna). As a result, the Frozen fandom is engaged in a brutal series of shipping wars, with the primary combatants being Kristanna (Kristoff/Anna), Jelsa (Jack Frost/Elsa), and Elsanna (Elsa/Anna). Jelsa, Helsa, and Kristanna tend to be more popular with preteens and teenagers while Elsanna is popular with the Periphery Demographic of adults. There's been a bit of ship combat from people who are disgusted at Elsanna, dislike Jack Frost (or just Elsa with males or Crossover Shipping), can't sympathize with Hans (or can't understand how Elsa could love someone who tried to kill her and her sister), or don't think Kristanna had enough proper development in the film to like.
Probably due to the very small cast, the Maleficent fandom is relatively peaceful - the most common ships are Maleficent/Diaval and Maleficent/Aurora, and they have a different target audience. There is also Aurora/Philipp, which gets along well with Maleficent/Diaval, and, an outlier, Diaval/Philipp, which again has a different target audience than all of the above. The most heated debates are about whether one should ship Maleficent with Aurora - some think it borders on incest as the characters were so close when Aurora was still a child, others say that that's just another excuse to Hide Your Lesbians. As all the shippable (i.e. not evil, non-human or very unimportant) characters are portrayed positively in the movie, there seems to be no debate as to whether people deserve each other - the worst accusation against Philipp is boringness, and in lesbian shipping he's usually allowed to hang around the main characters as best friend. Same with Diaval. And then, of course, there are those who ship all the main characters together..
The first popular ship to emerge from The Force Awakens was Finn/Poe. Fans commented on the bromance between the two, praising their on-screen chemistry. This has mainly brought them at odds with those who think Finn would be better paired with Rey, and the two groups have gotten into many debates as to whether a same-sex or interracial couple would be more progressive on the big screen (expect homophobia and racism accusations between fans). Not long after the film was released, however, Finn's actor, John Boyega, issued a statement declaring Finn/Poe as strictly a bromance. This has not stopped fans from supporting the couple. With Finn/Rey recently sunk via another recent interview with John Boyega, the potential for a Poe/Finn romance would seem more likely.
The other primary pairing to come out of The Force Awakens was Finn/Rey, a pairing that was teased throughout the film with their mutual rescues of each other, Finn asking if she has a cute boyfriend, their mutual desire to stay together, Finn coming back for Rey like she wished her family would, their emotion-fill hug, and Rey's vow to return to Finn before kissing him on the forehead. As of The Last Jedi, Finn/Rey shippers point to Finn waking up from his coma calling out for Rey, Rey trying to get ahold of the Resistance to check on Finn, Finn holding the beacon (along with Leia) that would lead Rey home, Rey telling Chewie to pass on a significant message to Finn that the audience isn't privy to yet, and an emotional reunion hug, as reasons for why Finn and Rey will be considered canon. Many of their fans interpret Rey seeing Finn and Rose together as being jealous and hope for a love triangle between the two. The topic of racism is touchy with the shippers—while there is a Vocal Minority who genuinely don't ship it for racist reasons, most who don't just prefer other ships. Meanwhile, there's a Fan Dumb portion of Finn/Rey fans who accuses anyone who doesn't ship it of racism and even throws unwarranted abuse accusations and insults.
More popularnote this AMV had over a million views at the time of this posting, one month after its creation is Kylo Ren/Rey. The pairing became favoured after viewers were intrigued by the characters' on-screen sexual chemistry and intense interactions—even Time magazine's review of the film commented on it. However, the ship has gained its share of disapproval, mainly from Finn/Rey fans who allege that the relationship is abusive or unhealthy. However, Kylo Ren/Rey fans express that they do not support the pairing as it currently exist in the canon, but rather suspect that Han and Leia's son can—through Character Development and a potential HeelFace Turn—embrace the light and begin to atone for his innumerable sins. On the other hand, the anti-shippers believe that murdering Han Solo was too big of an act to overcome. Arguments have arisen frequently on the subject of Kylo's "redemption", with some of the nastiest ship-to-ship-combat surrounding Finn/Rey fans calling Kylo/Rey fans racist for supporting that pairing over the interracial Finn/Rey and for making racist remarks about the ship. Gasoline was poured on the already raging fire when John Boyega (who plays Finn) not only confirmed in an interview that Rey and Finn are just friends, but that the romance in The Last Jedi is "not going to go the way you think it's going to go". The anti-shippers have since resigned to arguing that they won't trust John Boyega's words until The Last Jedi is released, and that no matter what the Kylo/Rey pairing would be too controversial. The Last Jedi changes the fandom landscape by pushing Rey/Kylo from a niche ship to one of the major players. There is definitely sexual tension present, which of course only encourages the shippers: their intense vision scenes, specifically the scene where they touch hands, Rey being Distracted by the Sexy upon seeing him shirtless, Kylo asking him to join her with phrasing evoking a proposal, would seem to encourage this ship. However, whether there will be a full-fledged romance is yet to be seen and they part ways on a sour note due to Kylo, despite having killed Snoke, still not on board with turning to the light yet. Combined with the revelation that they're not related at all, debates over this pairing have only intensified.
Add Ho Yay Kylo Ren/Hux into the equation and the mess gets even bigger.
Finn/Rose becoming canon as of The Last Jedi adds fuel to the fire. Once The Last Jedi was released, some particularly toxic Finn/Rey shippers went as far as to throw racist remarks at Rose and the actress who plays her (ironically supporting the racism they claim to be against). Some of them even claimed that the Vietnamese Rose is a "downgrade" compared to the white Rey as a love interest for Finn. The fact that Finn/Rose and Rey/Kylo shippers tend to be Ship Mates also increases the tensions between Finn/Rose and/or Rey/Kylo shippers and those who ship other pairings.
To sum it all up, the current shipping war consists of the following: Kylo/Rey vs. Kylo/Hux vs. Finn/Rey vs. Finn/Rose vs. Finn/Poe.
The Star Trek (2009) fandom is split between Spock/Uhura, the Official Couple, and Kirk/Spock, the grandaddy of all slash pairings. Some of the fighting has gotten very nasty, resulting in some very homophobic remarks from Spuhura shippers and accusations of Abrams "pandering to middle America" from Spirkers, as well as some racially-tinged Ron the Death Eater directed at Uhura.