Since a remaster is not a remake a remaster shouldn't change too much but instead fix bugs, errors or blatant design flaws but keep as much of the game "as is". In terms of controls or modern features like quicksaves, higher resolutions etc. I'm all for progress and these things should be included if feasable/possible. Quality of Life enhancements should be optional so you can have the pure experience if you want to.
A remake, like the above mentioned Spyro remake or the Demons Souls remake, should be viewed differently. Often the graphics improve dramatically, new assets, a new engine etc. create almost a different kind of game and the developers should be very careful not to diverge too much from the original. Something that can break the experience for me for example would be whole new expansive questlines about minor characters that don't interest me, a lot of meaningless content just to make the game bigger or even a change of the voice actors or iconic sound effects into drastically different directions from the original game.
A remake that I couldn't get into for the life of me was Final Fantasy VII. The cardinal sin to me was that it was wasting my time with boring minigames derived from offhand little things from the original game and expansions on characters or world elements that I didn't have any interest in. I get that this is different for different people but the FF VII remake was a slog for me after a certain point. The Midgar section that in the original game takes around 5 hours is stretched to 40 or 50 here which felt unnecessary and a little directionless.