Canon and continuity do matter. It's just competent storytelling, and it's all one unfolding story. However, they make mistakes and you just do your best as a viewer. They do change details later, sometimes because a bit of continuity was no good and was holding them back. Most of the personalities on DS9 had to change. The later changes usually have to be honored, at least when they work and don't screw things up.
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Viewing while caring about the long term story requires a flexible mind. You overlook the stuff they changed.
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As for Discovery, it not only should be viewed as another timeline, it actually is another timeline. I know many people see red when this is brought up, but there's reason to believe they began with DSC as a reboot and started saying it's part of the main timeline so as not to alienate fans. So they've massively altered things and then say there's no conflict. Well, there is. Look at it. End of argument. Silly to revive the look of Pike's original era? Of course not. The same style with more detail would be great, and obligatory if you're going to set Trek in a very specific past era. They didn't have to set it then.
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It's a reboot. Problem solved. Enjoy.
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It's fine not to care about continuity.... but "You're an idiot if you care"... obnoxious. Put up with it. We're not you.