I'm in this thread defending Arya and calling Jon Snow a Mary Sue, so you know I have no bias against female protagonists.
But Rey is 1000% a Mary Sue. She screams shytty fanfic self-insert like that one girl from twilight or any number of young adult novels by a female author.
Luke started out as a wide eyed naive nobody, he was functionally useless for large portions of the entire first film. At the start of the second he almost died on Hoth and needed Han to rescue him, loses to Vader and loses a hand. It isn't until the third film he becomes a badass only after receiving training from Yoda the GOAT Jedi and Kenobi. Luke has the GOAT Hero's Journey rendition on film.
Anakin is the chosen one, he should have reason to be a Mary Sue but even then, in the second he loses a hand because of his cockiness and in the third he loses everything because of his fear and paranoia.
Now Rey. Don't even get me started on Rey and her absurd advancement in the Force. A Mary Sue is always the most important person in the room. Why, in the ever loving fukk, after hearing that Han died would Leia hug Rey instead of consoling Chewbacca? Why does Luke, son of the chosen one, who faced off against Vader and Palpatine say he's never experienced power like hers before? Name any character flaws that Rey has? What are her motivations? Why is she good?
Not only is she a Mary Sue, she is a disgustingly bland character. She's Jar Jar status.
The Force is never depicted as your average superpower which is mastered quickly, it takes years of training to become proficient even if you are talented.