Spider-Man: The death and replacement of Peter Parker in the Ultimate Comics definitely polarized the fanbase between those who like newcomer Miles Morales and those who want him gone and Peter back.
Green Lantern. God help you if you try and discuss who is the best Green Lantern; the fight between fans rallying behind their preferred Lantern is one of the most persistent in fandom. Major factions include old-school Hal Jordan fans/Superfriends fans who feel his character was assassinated by turning him into the supervillain Parallax during the Zero Hour event, Kyle Rayner fans who feel that he's the most creative user of the Green Lantern ring (and that Hal was a bland character with little personality), and fans of Justice League/Justice League Unlimited cartoons who were first introduced to John Stewart and wonder why comic book fans are arguing about two white guys when Green Lantern is a black ex-Marine.
Batgirl: Fans are split over their preference for BarbaraGordon, the original Batgirl, or her Darker and Edgier replacement Cassandra Cain, or her Lighter and Softer replacement Stephanie Brown. Further complicated by the fact that Barbara Gordon fans are split between those supporting her uncrippling and those wishing it happened again. There is always been an Unpleasable Fanbase since Cassandra Cain first took the mantle, and now that 3 fairly popular and quite different characters have had the role, it gets worse, even though all 3 have had successful times under other monikers. Which meant that if DC had simply provided all 3 with a consistent role, they could probably avoid such difficulties, but replacements cause the replaced to be Put on a Bus and ignored.
Supergirl: The fanbase is polarized between fans of the original Supergirl Kara Zor-El and fans of the other Supergirls that DC spent eighteen years attempting to replace Kara with. Kara's fans feel she's the only Supergirl who actually makes sense, worked fine during twenty-six years until DC killed her off, and her death and failed attempts to replace her with short-lived substitutes led to a gigantic Continuity Snarl. Other Supergirls' fans think Matrix, Cir-El... are better characters and resent Kara's increased popularity and exposure since her return in 2004.
Superman: Crisis on Infinite Earths and the 1986 reboot splintered the fandom and the rift hasn't yet healed after several decades. The real identity is/should be Clark Kent or Superman? Superman should be able to move planets or only mountains? He must be the only survivor of Krypton or characters like Kara Zor-El, Krypto the Superdog and General Zod are essential to the mythos? Krypton provides excellent world-building and storytelling opportunities or must be reduced to mere background excuse for the powers? The debates will NOT stop.
The Punisher: Depending on which comic fan you ask, The Punisher Kills the Marvel Universe is either an awesome one-shot for having the Punisher kill every hero and villain in the Marvel Universe or is an awful Author Tract from Garth Ennis (who is notorious for disliking superheroes) for having many of the heroes' powers Nerfed so that the Punisher kills most of them effortlessly and the Punisher coming off as Unintentionally Unsympathetic for not considering that the heroes are people behind their masks until he's killed all of them.
Wonder Woman being the biological daughter of Zeus in the New 52 has been quite the hot button topic among fans. Some see it as an interesting twist and updating of the character while others see it as a violation of everything Wonder Woman was ever meant to represent. It also destroys the associations between Diana and her former patrons (Athena, Artemis, Aphrodite, Demeter, Hestia and Hermes) and Zeus who was always a misogynistic borderline villain for her, and has tried to rape her.
Likewise, her not being made of clay anymore (instead being a normal birth) is a heavy topic but not nearly as contested as making Zeus the source of her powers.
With exceptions of Marston's, Greg Rucka's and George Perez's runs, which are mostly beloved and Merdith's Finch's and all Wonder Woman runs in her third volume prior to Gail Simone's, which are generally disliked, all runs on Wonder Woman fall under this as a whole.