Yeah, I knew there must be a debate about this in the comments the moment I saw it.
Honestly, I personally disagree with the sentiment on all levels. Meaning, I agree with your observation that there are degrees to "restoration", and fixing a mistake is just not the same as changing music.
But then, I also have no sympathy to your objection of changing music or replacing a puppet with CG. I mean, I may like the old take better, but whatever, I'm not the one who made the movie. The people who made this particular cut for this particular release made it (duh). And these may or may be not the same directors and producers that made the cut you consider "the original one". It's their vision. Surely, it may seem surprising to a naïve viewer that it's not the director the movie is attributed to who "made it" in its entirety, but this is just never the case and obviously any cinema enthusiast knows it all too well anyway.
(But then I should probably mention that my fundamental disagreement with the sentiment spreads way farther than that, and I myself consider it kinda extreme. I often would be fine with the kind of "restoration" that essentially destroys the original thing. This would be off-topic to explain it here, because it wouldn't be about the movies anymore, but I just think that too much respect for the great things of the past often leads to losing sight of why these things were made in the first place. They were meant to be great at the time, not to be respected as a very old pile of rubbish a couple of thousands years later.)
The only thing I am kinda objecting to is when changes made reflect the current political agenda in one way or another (i.e. censorship, be it taboo on display of tits on TV, cutting out statements that seem "politically incorrect" at the time and place of the release, removing some persona non-grata who made a very minor cameo appearance in the original movie or anything else like that). But, again, I don't really object to that because "they don't have the right to do it", but because it's just irritatingly stupid and makes me roll my eyes. It doesn't necessarily make the movie worse or even substantially different (I might not even notice), but unlike with remastering of the original movie, the intent clearly isn't to make it "better" (in their opinion), but just acting out of fear to cause trouble by displaying today something that was fine yesterday as is.
What I think is kinda lacking is very clear and non-ambiguous versioning of movies. I am not that much of a movie enthusiast myself, but some people obviously care if you can see the original number-plate falling off the car, and it would be nice if these people could easily refer to that particular edit they like better. They kinda always do it anyway, but that only happens if they need to specifically mention this number plate falling off, and normally they try to pretend that 10 edits made for 10 releases on different media in different countries are all the same movie, which (almost by definition) is not the case. I mean, for books we have versions and ISBNs, and it's normal to reference specifically that, not just one of the authors and the title. Should be standard practice for movies too.