In retrospective, I think that a good bunch of the false accusations against SK aren’t so much misconceptions as they are people either misremembering things or assuming stuff. I mean; Naruto is a weekly manga, after all. Take Chapter 415 for example. It happened in October 2008, and I bet that not many people have re-read that chapter in the past few years; all they probably remember is that Sasuke saved Karin once, and that’s that.
But all the details - his desperation, that he actually awakened a new power for her, that he risked his and Taka’s lives, so on so forth - are all a blur. They might have gone “?” at the chapter back when it came out, but they haven’t feel the need to re-read it since then and taking what happened in 480 and 481 at face-value probably overrode anything positive that might have stuck in their minds concerning Sasuke->Karin.
Cue why there are the silly claims about Sasuke saving Karin due to Team 7 and the assumptions that Sasuke only regarded Karin as a tool, nevermind how nonsensical the latter is in and of itself thanks to the simple fact that he valued her life above his own - thus, above the mission she was meant to be a “tool” for.
Then there are the more general assumptions; those regarding Sasuke’s character.