The problem is when learning new things about them makes them into different people.
Sometimes characters change as writers develop them. They may be different people in the pilot than they become later on as their characters evolve. Spock himself is an example -- the Spock that developed over the series wouldn't grin at a chiming plant like he did in the first pilot, or be as devoid of telepathic ability as he appeared to be in the second pilot, or be as sanguine about killing the last member of an alien race as he was in "The Man Trap." Similarly, Data was originally written as having emotions. I'm currently rewatching a show (
The Middleman) where the lead character is willing to torture a suspect for information in the pilot, but evolves quickly into a much more wholesome and moral character who refuses to let a predecessor torture a suspect just eight episodes later.
It's the prerogative of creators and performers to discover their characters as they go, to try things out and find what works and what doesn't. It's a process of refinement that often leads to changes in how the characters are portrayed, especially as characters are adjusted to fit their actors' personalities. Sometimes it's for the worse, e.g. when a comedy character gets progressively dumber or more caricatured, but sometimes it sands off the rough edges and makes them better characters. It's not a problem, it's just how creativity happens. It's just that when a character made only one appearance decades ago, or a handful of appearances, our image of them is more locked down when they're brought back and developed further, so it feels more drastic than when a regular character changes between the pilot and finale of a single season.
The problem with being too fixated on consistent continuity is that sometimes consistency gets in the way. Sometimes early ideas are not the best ideas, and being slavishly consistent with bad ideas is not good for a series. It can be a good thing to change a character or a story point into something better and just gloss over the original, inferior version.