First, a Mary Sue character is a wish fulfillment character. The idea was born from fanfiction and came into the main when this type was noticed in mainstream media. A Mary Sue cannot be a main character because part of the definition is that they upstage the main character. Wesley Crusher was almost a Mary Sue with how often he saved the day. Rey is the main character of the ST. She can’t upstage herself. When we meet her we are shown that she is a skilled fighter. She had abandonment issues. Throughout TFA she just wants to go home and wait for her parents until she finally accepts that her life is taking a new direction. She doesn’t just randomly pick up any force skills (which we are never shown are that hard to learn if you believe you can do it, which was Luke’s problem). She does not pick them up perfectly on the first try any more than Luke picked up blocking blaster bolts the first try. In the OT we went through the heroes journey in the first film before resuming it in the second. Here we are following Rey on that journey and she isn’t zooming through it in one film.
In TLJ she enters the training part of her journey but ends up with Luke not wanting to really teacher, instead he is trying to scare her off. It doesn’t work. Rey steals the sacred texts and leaves having picked up enough to work with. She knows she is powerful and needs training. What she lacks is not ability, but focus and purpose and she gets that in TLJ. By the time she gets in front of Snoke, she has some false confidence and would have been killed if Kylo wanted her dead, but instead he kills Snoke and Snoke’s guards attack. If you watch the scene, Kylo is the better fighter. He fights more of them and against tougher odds. When it comes to the raw power of trying to grab the saber with the force, they are equal. Saying she won when she did not accomplish her goals for going there is ridiculous. She basically failed in all her goals for TLJ. She did not get Luke to come back (Yoda did). She did not get Luke to teacher (he gave her some minor lesson and she stole some books hoping she might learn more from them). She did not turn Kylo. And her saber is broken. So for Rey, TLJ is a list of failures an if she was a Mary Sue, she would have had some big successes other than lifting a bunch of rocks (something that could have been done manually by Chewbacca).
Rey comes closer in TFA, but when you compare where she is at in her heroes’ journey compared to Luke, she has only reach Mos Eisley by the end of TFA and just escaped the Death Star by the end of TLJ. We knew Luke was a great pilot and he picked up the force power that Obi-wan taught him in just a few minutes so Rey being a great fighter, mechanic, and pilot (Luke had all those same qualities) isn’t so different from Luke. But Luke had a much longer and more convoluted journey because when Star Wars came out in 1977, it could have been the only film that ever got made so Lucas gave Luke a complete journey in one film and then reset and resumed his journey in TESB. Rey is missing that journey are reset and is just on the heroes’ journey (it starts with the call and the rejection and the eventual acceptance (TFA) followed by her training and some trials (TLJ) before her chance to save the day arrives.
If Rey is really a Mary Sue, the success of her side in both films would rest with her and I don’t see her provide that success. For Rey to face Kylo in IX, she has to be as good as he is. So she is a protagonist to match him as antagonist. Her story is not one of constant successes. She has failures. She learns the force fast, but as far as we have seen that is normal, as long as you believe you can. So the force doesn’t come easier to her than it did to Luke or Anakin. That is an assumption that is not based on events in the previous films. Luke had problems believing, never a problem with actually doing once he believed he could. And Rey sees Kylo do these things before she does them. She doesn’t have to take it on faith like Yoda made Luke do with the X-wing. And when she attacks both Kylo in TFA and Luke in TLJ, she has surprise on her side (not to mention Kylo being wounded). She never bests either of them in a fair fight.
A Mary Sue would be the best and would always win. Things would always go her way. Instead she spends all of TFA wanting to go back to Jakku and being prevented and spends all her time in TLJ with goals that don’t pan out. So far the only thing she has done successfully is locate Luke. Equating her fast learning of the force with being a Mary Sue ignores all the plot that matters. She spends most of both movies looking for a mentor only to come to the conclusion that she will have to teach herself, there by growing past her need for a parent/mentor. Rey is beset by issues that keep her from being the answer to all the problems.