The biggest one everyone seems to be forgetting about is that Mary Sues are author inserts. That is, Mary Sues are characters inserted into a story (usually an existing franchise or fandom) for the author to live vicariously through them.
I don't think people truly get it: Mary Sues are perfect characters. I mean, literally perfect. Very few of them actually exist outside of fan fiction, and even people that write fan fiction today are smarter than this (unless they're still in their preteens or something).
The very fact that Rey is even Palpatine's daughter does not make her a Mary Sue. If she was, she'd be the daughter of two incredibly powerful Jedi, one half 'human', the other half Twi'lek or something (I'm not a huge SW fan but I'm guessing Twi'leks are renowned for their beauty). She'd have completely unique features which makes her desirable to any and every guy (and they wouldn't stop talking about how beautiful she is) Every girl would like her too, but if there's one girl that doesn't like her, she'd turn out to be evil because Mary Sue knew she was and said so. If Rey was a Mary Sue, she most likely wouldn't have been a poor scrapper hustling for food. She'd be a young Jedi in training. She'd be the true chosen one, and she'd singlehandedly end the conflict by just existing and making everyone love and respect each other, because Mary Sue is such a good person that it rubs off on everyone. If Rey was a Mary Sue, she most likely wouldn't even be the main character of these films. She'd be the main character's love interest.
I say she came closer to it in TROS because she was revealed to be Palpatine's daughter and that movie wasn't well written, but even then she doesn't get there. Palpatine is evil, and Mary Sue's aren't born from evil.
Here are some good examples of how a Mary Sue would be written.
https://www.quora.com/Could-Spider-M...red-a-Mary-Sue
https://www.quora.com/If-persons-cri...-Sue-character
I agree that Rey is written in a way that makes how overt competence somewhat unrelatable. But being a power fantasy or a badly written character doesn't make you a Mary Sue.