I figure it’s fairly simple. “I am the biggest Star Trek fan! I am the truest fan! I love Star Trek so much that— oh, I don’t like this bit of Star Trek. And yet, I am the biggest fan. That must mean —this isn’t really Star Trek! I, the gatekeeper of all true Trek, banish this from the True Trek!”
You can change just a few words and get the version for people who love all Star Trek but don’t bother with the books and comics and get dismissive about how they’re just a waste of time because they aren’t canon.
I think you have this absolutely right. This is one of those things that has always (and continues to) utterly baffle me. I don't particularly like TOS or Enterprise, but I don't believe I've ever for a minute thought, let alone stated, that they aren't true Star Trek just because I don't like them much. I can't even imagine how I would reach that mental space.
And yet the number of times people have told me that I'm not a real Star Trek fan because I (a) like Discovery or (b) only grew up with TNG is probably at least above twenty. My favorite: "It's fine if you like Discovery, but let's be real. Those of us who grew up with Star Trek just get it in a way young people can't. It's OK if you're one of the latter.

