Note: This article lists examples which take place within fandoms; not the TV Trope's opinion as to whether a change is for the worse. TV Trope doesn't have opinions. The focus is on over-reaction about minor changes.
Generally, in any rendition of a Shakespeare play, there will minor to major deviations from the "original" script that can result in any given theater-goer declaring it ruined. Even something as minor as changes in tone or cadence from what is expected can offend. Slightly justified in the fact that a change in tone can result in a change in the entire interpretation of a speech.
The ancient Roman playwright Terence adapted six Greek plays. All after the first contain "prologues" in which the playwright rants at the audience about criticisms of the previous adaptation. Apparently, the Romans accused him of "contaminating" the original plays by changing plot elements or tones, and at one point an audience even walked out after it became clear he had combined two similar but separate Greek plays into one adaptation.
Stephen Sondheim just loves to tinker with his musicals even after their initial productions have finished previewing, resulting in different audiences seeing different versions of each show. None of these changes are supported by all the fans, but the most controversial is the addition of "Something Just Broke" to Assassins. Depending on who you listen to, it's either the master stroke that pulls the whole thing together, or a disastrous break in the dramatic arc that should never have been added and should be erased from existence.
Even more controversial were the changes made to the 2002 revival of Into The Woods. Assassins, at least, has always divided both fans and audiences and has widely been regarded as a problem show; Into The Woods, on the other hand, is one of Sondheim's most successful, popular and beloved works as a composer-lyricist. The decision, then, to reintroduce a totally unnecessary (and not very interesting) sub-plot about the Three Little Pigs, as well as replace several existent and already excellent lyrics with new (and, according to some tastes, inferior) ones, seems baffling.
Sticking with Sondheim, John Doyle's actor-musician revival of Sweeney Todd: The Demon Barber of Fleet Street has enjoyed huge success and popularity with fans and critics alike, but its minimalism continues to rub some fans the wrong way. Some say that the score suffers in reduction from a full orchestra and ensemble choir to just eight actor-musicians; others found that Doyle's alienating production style prevented them from identifying with the characters.
This take was lampooned by the Forbidden Broadway cast, by the way, as "Teeny Todd."
There's also the matter of the London version of Follies, which made several baffling changes. Ben's solo "The Road You Didn't Take" was cut. "Live, Laugh, Love", was replaced with "Make the Most of Your Music" (a song which changes Ben's part from baritone to tenor). The lyrics to "In Buddy's Eyes" were altered.
Wicked. Sweet Oz, Wicked. Though it should be said that while the purists of the book are infuriated with the many changes made to the musical, Gregory Maguire himself still likes it, and in fact stated that as long as the themes of the book were kept intact, the plot could change in any way necessary. After all, the book itself made changes to Baum's Oz...
An attempt was made to update iconic anti-Vietnam war musical Hair to reflect modern wars. Not only did making that change disrupt the entire show, since amongs other things the hippie culture is not prevalent and there is no draft to rage against. Not only did these changes not sit well with fans, it flopped critically, and the 2010 revival was much more faithful to the original
Of course the 2010 one bombed too, but that had different reasons.
Actor replacements. People don't seem to understand that the OBC of any show is unlikely to stay for the entire run. People will overly criticize the replacements, and claim that they ruined the show for them. Even if the replacement actors are better than the originals.