I don't know if most Trek fans get angry. I think people love to nitpick and we also find ways around mistakes in our head thus creating the concept of "head canon" but outright anger? Even with "Discovery" I think most of the outrage is less on the changes and more on the fact that want to put in the Prime universe instead of the Kelvin Universe or a 3rd universe. Basically saying it's okay to change things just not the Trek universe I grew up with.Someone used the word 'worship' on page one...
Canon/continuity is a good thing for any serial storytelling. No one's saying it's unimportant. The problem isn't the canon. The problems is the near religious approach some fans have with it, and how obsessive they become to make sure everything fits and how angry they become when ultimatly, something can't fit in.
It's like the reason why people don't complain about Vulcan being blown up or Spock and Uhura having a romance and in fact many of us like those things. The difference was this was all happening in another timeline and they weren't impacting the timeline from the other shows except for Romulus blows up and Spock spends the rest of his life in a alternate universe but those things usually don't come down to canon complaints.
Jason