If they find it entertaining enough they won't 'turn on it' due to continuity violations - Hell STII:TWoK is proof at that. It's considered the best of all Styar Trek films even with the fact that:
The fact a Federation Starship and it's sensors systems and crew FAILED to recognized the Ceti Alpha system had changed - and planet orbits shifted due to one of the planets in said system exploding - and somehow mistook Ceti Alpha VI for Ceti Alpha V.
The Character of Pavel Chekov was NEVER in the TOS S1
Space Seed episode (as the character hadn't even been created or cast yet when that episode was written or filmed); so there was no way Kahn could have seen his face to "never forget" it in the first place.
Khan himself is well aware of the actual year (2282) - yet when making his speech to Chekov and Co. says: "On Earth 200 years ago..." <--- Really? The Botany Bay launched in 1996. 286 years ago...what, did Kahn forget nearly a century? (And yes, I know the reason the line is as it is because in TOS S1 -
Space Seed; Khan was told on screen it was estimated that 2 centuries passed so that was a literal call back to the episode.) But yes, Khan can remember with clear specificity how many years ago he was left on Ceti Alpha V, and also when Ceti Alpha VI exploded, but he can't adjust now that he should know way more than 200 years have passed since he was a despotic dictator of an old Earth nation state?
The fact Kirk himself forgot about the fact that he HAS 'faced death' like he did with Spock - and did so in the second pilot episode of Star Trek S1 -
"Where No Man Has Gone Before", in that he was forced to kill his close friend of 12 years - Gary Mitchell (which he had served with and was friends with him to the point he asked for Gary Mitchell to be posted go the Enterprise, his first Command) <--- But of course didn't jive with the way the writers of
STII:TWoK wanted to portray Kirk, so of course Kirk forgot...
^^^^
yes, all these continuity errors, yet you don't see many Star Trek fans with torches and pitchforks decrying
STII:TWoK as 'not Trek' or it's producers and writers described as 'not knowing Star Trek history...'
Will the same 'Treksperts' on Youtube (like Small...er DoomCock et. al.) decry SNW as an affront to "Gene Roddenberry's Star Trek"? Absolutely. But overall Star Trek fans seems very forgiving if they find something very entertaining to them in a good way.