Here are a couple quick, low-effort instances where the issue of Rey’s parents might be toned down a tad. Sorry if the visuals are going nuts, not sure what that’s about, but it’s all conceptual anyway.

First, I cut Kylo saying that Rey’s parents chose to be nobodies “to keep her safe.” He instead just says they chose to be nobodies, which is implicit enough of some deeper truth (that he’ll reveal in two seconds anyway and that Rey seems to now remember) that we don’t need the follow-up “because they love you and were good people.” I mean, if Rey’s dad is Palpatine’s son and doesn’t want to be involved, he’d already be trying to pass as a “nobody” even if Rey didn’t exist, right? I think the result is far more ominous, and Rey’s lineage, not the love of her parents, is supposed to be the true “reveal” by the end of this whole sequence anyway.

Second, in the final confrontation, when Palpatine calls Rey’s parents weak, she doesn’t interrupt to imply that they were great people who she admires. Now, after Rey says she won’t give into hate, Palpatine just monologues uninterrupted. If the soundtrack audio with that cut is an issue (I don’t currently have the blu ray’s multiple audio tracks on me to isolate dialog), I think the faux-hopeful music that starts when Rey says “they were strong” could instead start when Rey says “You want me to hate but I won’t,” which would have the same effect.

Some other things that would be nice but I can’t try at the moment:

If Rey’s parents could not tell her “be brave” and “you’ll be safe” and all that, that would be nice, though it seems hard to cut/rearrange as we need to get a visual of them in that moment. Maybe just mute/distort their voices or something, like it’s a hazy memory? Maybe it’s not even a big deal.
Kylo actually mentions Rey’s parents being noble twice: the first is the edited clip I posted, but then he does it again later when he says “they sold you to protect you.” I don’t know if it’s possible, but I think a great way to edit this to de-emphasize Rey’s parents would be for Kylo to say “they sold you to hide you.” This means basically the same thing, but can be interpreted by the audience in potentially less loving ways; they hid Rey to try to save themselves, or they hid Rey to fight back Palpatine, or even they hid Rey because they feared her (which isn’t totally incompatible with their tearful goodbye).