As for how people on this site “cope” with the problems you mention, well a lot of people here just ignore the prequels, which are the cause of the majority of continuity problems with series to begin with.
I’d argue that the ST betrays the spirit of the series more than the PT did though. And that’s a larger problem than things like why Owen didn’t recognize 3-P0.
TFA is a waste of 200 million dollars because it copies a movie but makes it worse (And the argument that the first Disney SW movie needed to feel “familiar” is moot, since TFA locks the entire trilogy into a “big bad Empire vs. scrappy rebels” redo, complete with locking in the stale aesthetic/art direction), and TLJ writes Luke so incredibly OOC that he can’t be considered the same character who said “You’ve failed, your highness. I am a Jedi, like my father before me.”
You made this thread to talk about (seemingly) continuity errors. If the ST doesn’t fit your personal canon, I think we already have a thread to discuss that. If not I don’t know what to tell you.
Not exactly continuity errors, but more “How are we supposed to believe that all these movies have happened in the same universe when some filmmakers/showrunners are at war with sections of the saga”. And it even applies to things like TLJ throwing JJ’s mystery boxes into the garbage.