I propose there is three levels or stages of change, ranked in severity.
Level 1: Changes that radically alter how a PC functions or its place in the world. Player characters to me at personal, and radical changes to what a character can do or are reflect harshly. For example, a character who was an assassin in 1e doesn't feel right under 2e's "thief with the assassin kit" because the things that made him an assassin (death attacks, weapon/armor choices) aren't there. The same is true for changing tieflings appearance, or giving all high elves teleportation. It changed what those characters were. Generally speaking, radical changes to classes (including removal of), races, or spell mechanics (such as the removal of Vancian casting) fall under this boat.
Level 2: Changes to the Story or World. This is changes beyond the PC that rules no longer would allow for. For example, if one of the iconic stories of your game was a fight with a blue dragon in a sand-covered pyramid in the middle of desert, but the rulebooks now say blue dragons and coastal and semi-aquatic; you have mis-match of story and canon assumption that can't easily be explained without ignoring one or the other. Changes to monster mechanics, magical items, or core game assumptions (like wealth per level) fall into this.
Level 3: Backstory or minor changed: This is the level where, unless it affects level 2, can safely be ignored. Few people care what a mind-flayers origins are as long they fill the same role in the game. Or if the Abyss is under the elemental planes or next to Carceri if all you need is a few vrocks to fight? Or if orcs are Lawful or Chaotic as long as they are evil and guarding pie? These changes might annoy sticklers or purists, but as long as things function mostly as they did before, few people care. Changes to monster lore, world lore, or background game material fall here unless they end up affecting PCs (level 1) or the game/story (level 2).
So for me, giving my previously unmagical elf rogue the natural ability of teleportation is a major, radical change because it changes who he is. I'm less concerned that the succubus he fought at level 7 was hanging around demons when she should have been hanging around devils, and I'm only minorly annoyed that the demons she was hanging around with are corrupted elementals.