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.
The Oldhammer movement for Warhammer. The Oldhammer players stick to Warhammer 3rd Edition, which is universally considered as the most comprehensive and thorough of all Warhammer Fantasy Battle rules releases, and play it with the appropriate army lists. WHFB 3rd Edition was published 1987.
For Warhammer 40,000 players, "They Changed It, Now It's Heresy" is practically a warcry for the fandom. Every time a codex is released or some lore is changed, there is a massive outcry. A huge backlash came from Matt Ward's revision of the Necrons. Many players did not appreciate the removal of a lot of the scary aspects of their lore, as well as the removal of well-liked units, such as Pariahs. The third design for the Citadel paint pots had a screw top. The top would either get stuck from dried paint, or they'd fail to close properly due to dried paint. Needless to say, the design was awful and the outcry was enormous. When Games Workshop realized that people were buying paint from third-party sources, the classic flip-lid was re-introduced and remains to this day.
Among the Magic: The Gathering changes this has been applied to: The Sixth Edition rules changes, the Eighth Edition card face changes, removing Armageddon from the base set, making counterspells more expensive, moving from "Xth Edition" to "Magic 20XX", the Great Creature Type Update, the creation of Type 2, the name change from Type 2 to Standard... and so on. The new visual design of Slivers. Going from alien creatures to weird humanoids. Of special note is the heavy rehaul of the game rules in Magic 2010 (especially related to the combat damage mechanics change), which caused an enormous amount of furor and backlash, and miles of angry blog posts. The resistance to these changes has mostly died out, although some die hard fans of the older rules still persist. The new change to the legendary and planeswalker rules in Magic 2014 also immediately caused a storm of protest, although overall in a much lesser extent.
Among more legitimate complaints, this comes up a lot when Dungeons and Dragons editions are discussed. The base is not so much broken as it is shattered into a billion tiny splinters. Every single edition changed it and it sucked every single time. Not just Editions. Errata. Adjustments and changes to how powers work can set the forums exploding with "Class X is worthless now!" Complaining about nerfs to characters, in which people might have invested a lot of time is perfectly legitimate. Particularly as, depending on the edition, many/all builds rely on a very limited array of tricks and nerfing even one of them can push a character below the ability that the game assumes to be appropriate for his level. The trend from AD&D through 4E has always been about where to sacrifice verisimilitude to accommodate game-playability. Barring poor testing, the later editions are more mechanically balanced at the cost of things actually making sense from an in-game perspective. The feud is always about how far in either direction is "too far", with most people siding with whichever edition they started with. This trope combined with Broken Base makes D&D less a game system and more a collection of games with similar concepts but are ultimately separate in reality. The announcement that work is being done on writing future a 5th edition that will have modular rules as its selling point seems to be a case of Wizards of the Coast attempting to capitalize on this division. One specific D&D-related example: This review of the D&D-based Facebook app Heroes of Neverwinter. Many of the comments call the reviewer on it.
When people on the Privateer Press forums found out that one of the newest units for Warmachine was going to be plastic instead of metal, reactions were... mixed. Many people welcomed the change but a particularly vocal minority condemned it for straying from the "Full Metal Fantasy" aesthetic that the company had cultivated up to that point, among other things. It's either something to do with a feel of solidity, or the vocal minority use their Warmachine figures as sling ammunition and don't want to have to correct their aim. For those curious, resin-plastic warjacks do still feel plenty solid. Probably helps that the torsos are all one giant block of solid resin-plastic rather than being hollow like some of the walkers from another game.
Shadowrun, Fourth Edition was announced. And there was much rejoicing. Then the fans found out that the mechanics that have been in place for the last 20 years would be dumped for a somewhat simpler, nWoD-like system (though not quite as forgiving as the system described above). Cue half the fanbase going into instant-fury mode, which developed into major war between the pro-SR4 fans and the anti-SR4 fans long before the game was even released. Things have since calmed down, but in some SR forums comparison between #4 and the other editions is tightly regulated, if not outright "discouraged".
Earthdawn's Second Edition had this happen to it as well; in principle the changes to the system were instituted to fix the various broken things in the first release - ED players were subsequently upset that the update broke off backwards compatibility with said First Edition. "Show me the Lightbringers!"
The new edition of Hero System (aka Champions) has caused a fair bit of brain meltdown in its longtime fanbase, who have declared it not only sucky but completely ruined, and that all of their old stuff has been rendered completely unusable and there's absolutely no chance for it to interact with older versions. The only actual differences are the removal of an almost completely unused stat ("comeliness") and a single power type that almost nobody used anyway. The fact that dexterity is not the ultimate atribute anymore, that OCV and DCV (the stat that define how easy it's for you to defend and attack.) are now independant characteristic. Simply put, it's the end of the kung fu-ballerina-killer era.
An interesting variation occurs with every new edition of a Games Workshop game. Players will claim that the new edition is "dumbed-down" and aimed only at younger players, unlike the previous edition. This exact argument comes up every single time a new edition is released.
The 2011 Sisters of Battle codex has received a very negative reception. Most players felt that the already not-very-powerful Sisters went from "mid-low tier" to "absolutely unplayable." Some of the other changes really led to head-scratching, such as the new Faith system which gives an army 1d6 faith per turn - whether that army is a 500 point skirmish force or a 3000 point massive force. Complaints include failing to scale powers, confusing powers, and nerfing an underpowered army. They changed it so it's simply not even worth fielding. Players tend to ignore the codex update altogether.
The 2011 Grey Knights codex received an impressively negative reaction for going the other way; the Grey Knights were always liked by fans and considered overpriced before the new codex. The update included some atrocious fluff such as Grey Knights killing Sisters of Battle to use their blood as a holy oil to a chapter master who single-handed managed to bitchslap dozens of Cthulhus without trouble. Add in some absolutely appallingly powerful units, some confusing rules interactions, and models many gamers simply disliked (the baby-carrier Dreadknight) and the cries of Marty Stu and Game Breaker are far louder than those who approve. The errata did not help; it mostly confirmed that every attempt to abuse the Grey Knights' powers was legal.
This example could be made for Space Marines, Blood Angels and Necrons. EACH. They are all made by the same author including the two named examples.
Imperial Guard and Dark Eldar seem to have evaded this in part because the IG were the buttmonkey for the previous 2 decades and their new codex gave them teeth without being overpowered, and the Dark Eldar codex was 14 years out of date and really didn't change anything significant it just made them consistent with 5th edition rules and more playable but still the hardest faction, that is until the Sisters received their infamous update.
In a typical fashion, GW changed the models of the Daemonettes of Slaanesh, who originally were maximum The Eighties to an army of Cute Monster Girls. Male players approved. Then they changed them again and now they look less eightees but extremely hideous. Male players were not amused. Almost needless to say, the old models achieve record prices on Ebay.
Many fans of the original World Of Darkness games were outraged by loss of a metaplot in preference of a more personal focus (though the metaplot of the original games was a point of contention for many players). Still others were furious that White Wolf removed their favorite subgroups (even though most were actually included, if re-envisioned, reclassified, or renamed).
Battletech. There are still people who rant and fume about the Clan Invasion (which had been foreshadowed for a decade), the Jihad, and reconciling the classic game with the established Mechwarrior Dark Ages storyline.
A lot of the initial grousing that occurred when Champions went from 5th edition to 6th was originally chalked up to this... until someone started doing a serious analysis of the game and found out that, yeah, there were a lot of new rules that basically arbitrarily screwed your long-established characters, assuming you tried converting them from 5th to 6th.