It's because you have no idea what a Mary Sue is.  Which is evident in you not trying to argue away her status as a Mary Sue, but instead using ad hominem attacks against the opposing side, calling them sexist, and just naming random powerful male characters, without anything to back up that they are Gary Stus.

Neo is a freaking weakling at the beginning of the Matrix. He would have gotten his ass beat by a normal human, let alone an agent. He actually gave himself up because he was too scared to climb on the ledge, a very human thing. And no, the next scene isn't of him discovering his powers and busting himself out through a couple of agents. He actually has to be taught how to bend the rules of the Matrix and be taught how to fight. It isn't until the very end, after getting his ass handed to him, does he become the One.

Harry Potter has to be taught how to use magic. He doesn't get his wand and all the magic goes through him, making him close, if not more powerful than Dumbledore. He's not even shown to be the greatest student of all time. Hermoine is much better than he is. A lot of his power is due to his mother's sacrifice and Voldemort accidentally transfering some of his power into him. He's a good Quiddich player, yes, but I don't think they ever try to make him out to be the best. His first match he accidentally wins. Now, you may say a lot of lucky things happen to him and his friends. However, there's another term for it, called plot convenience. It doesn't make who it happens to a Gary Stu/Mary Sue. 

I'll admit that I haven't watched a lot of Bond films. The ones I have seen, he's already an agent, so it's obvious he's gone through some serious training. He's not going from just finding out about the agency to 007 in just one film. I've also seen him get his ass kicked and win by the skin of his teeth. Or be thwarted by the big bad early on, to have to defeat them near the end. Now, maybe some films portray him as infallible, but I haven't seen them. 

None of those appeared in one of the largest franchises with the same severity of Mary Sue that Rey is.

This is way too much of a quotefest jeez, but quick round-up

1) Crashing the Falcon would end the movie, and by Star Wars logic competence with a flying vehicle is competence with any flying vehicle (see Luke and X-Wings) and we know she has flown:
"I've flown some ships, but I've never left the planet" + She shows repeated familiarity with the Falcon's history and interior, suggesting she knows enough about it to fly it, if she hasn't flown it already ("That one is garbage")

2) "Mary Sue" delineates a near flawless character, but she's shown to have huge baggage and character flaws, unrelated btw to the larger Star Wars character roster. I.E. her past is not a way for her to perfectly fit in pre-existing story-lines, which is what the original Mary Sue point in fanfiction was about.

3) Yes, Luke and Han (at least initially). Can you read?
She's the hero, so characters ultimately trusting her, especially as she is a Force user and interested in joining the Resistance, just makes sense. 

The main cast has no reason to dislike her, so why exactly would they?!
As a meta point, she clearly represents the bright-eyed optimism of Star Wars fandom, so the main cast ultimately disliking her would kind of make the point that liking Star Wars is wrong, which is just baffling! 
It seems you want the main cast to dislike her because you do..

4) Are you suggesting a wounded Kylo Ren is as strong as Darth Vader? lol
Excusing that pile of nonsense, Kylo, who is bleeding out from both a gunshot to the stomach and a slash from Finn, is shown troughout to be the superior fighter. Rey barely manages to get a "win" over him by using the Force. A reminder that Kylo is trying to turn her to the Dark Side, not to kill her.
The movie is quite clear in showing that Kylo is stronger, and that the real fight isn't over yet. Like TFA will get sequels or something.

5) Ah, you really showed me here

6) The point isn't that I don't like the term, but that stupid people tend to like it a lot. 
Ergo, using the term makes you look really, really stupid.
Go on though, just saves me the trouble of taking you seriously

Did the Falcon crash? No. Okay, I can buy that.

What I cannot buy is that the Falcon would be able to outmaneuver multiple fighters considering its larger relative mass. That's like a cargo van outmaneuvering a race car or a B28 bomber outmaneuvering a fighter.

The Falcon was meant for smuggling, not maneuvering but in the hands of Rey, it can do anything.

Like I said, if you don't like the adjective then Rey is  overly competent to the point that credibility in her character and tension in the film are both destroyed.

Are you suggesting that in the act of liking/trusting Rey, the other characters break the fourth wall?

I'm expecting the cast to be neutral to her, not to dislike her much like how to Han, Luke was just talking cargo and to Leia, Luke was a means to escape. Even after all was said and done near the end of ANH, Han wanted to leave and Leia was getting back to work fighting the Empire. All Luke's connections got him was joining with other X-Wing fighters in a daring attack on the Death Star.

Compare that to Finn who devoted himself to Rey or Rey getting a critical lone mission to find Luke. Rather than the rebels sending a delegation to meet Luke in this vital mission, they send a newcomer on her own. Compare that to Kylo who is trying to recruit her to his side. Vader was aiming to kill Luke in ANH.

No, I'm suggesting a wounded Kylo Ren should be able to at least render helpless a novice Rey who just recently discovered the force and just recently wielded a saber. Instead, she wins and the tension in the scene is destroyed. Kylo Ren's threat level is destroyed. I'm not invested anymore because Rey just keeps showing she always comes out on top no matter the circumstance.

Is it so much to ask for that the protagonist get his/her ass kicked a bit and lose here and there much like with Luke? Give the opposition a bit of a threat level rather than removing it.

Rey is overly competent to the point that credibility in her character and tension in the film are both destroyed. How's that?

This bears repeating btw:

I think there's an angle you're not seeing here. I'm sure you could provide reasons as to why Rey always seems to have the upper hand in whatever situation she finds herself but this doesn't change the fact that she always has an upper hand. No feat seems impossible to her.

This is a problem for storytelling: things like building tension and helping the viewer to suspend their disbelief are done by not only making a character believable but also making the antagonist threatening. Rey being good at so many things at some point becomes unbelievable.

I think everyone here would agree that they're good at some things and bad at other things. I'm good at math and science but I'm terrible at reading Shakespeare. That stuff is not modern-day English. Even people really good at one thing are not so good at another: Michael Jordan was a great basketball player but a mediocre baseball player.

Being able to fix things, speak droid, fight well, and even overcome Kylo's mind probe and turn it against him runs counter to building tension because at some point, I just expect Rey to always win. Rey being good at everything isn't gonna make me wonder if she'll be able to overcome the next obstacle, I'll just get used to expecting it.

That's boring: tension dies and suspension of disbelief is shattered. It's what happens when you turn on god mode in a game: fun at first but it gets boring quickly. Without risk, where's the fun? Where's the challenge? Would a game that was won by pressing a 'press to win' button be fun?

No, it wouldn't be fun.

To add to all this, this latest Star Wars trilogy does not exist in a vacuum and neither does Rey's character: Luke Skywalker exists in this universe and he had to get his ass kicked before becoming the capable Luke Skywalker in episode 6. He got his ass handed to him by cantina thugs, tusken raiders, Darth Vader, and even the emperor rendered him helpless with lightning.

Thankfully for Luke, he had people to help him: Obi-Wan rescued him from cantina thugs and tusken raiders, R2 and 3PO saved him from getting squashed, Han Solo saved him from getting shot down in ANH and freezing to death in ESB, Leia saved him when he was close to plunging to his death in ESB, Darth Vader saved him from the emperor in RotJ.

Rey saved herself when in the same film, Poe needed help from Finn and Finn needed help from Rey. Doesn't seem terribly balanced.

Harry actually had to learn in school, and his ability to deal with Voldemort was given to him by his mother. Rey equals Kylo because the force demands equilibrium. So, why did Luke have to train and work his way up. But Rey gets free passes?

Neo isn't a weakling at the beginning of the Matrix. He fails the first jump but that's it. He only fails because he doesn't trust in his inate powers. 

The very first time he spars with Morpheus it's clear to the audience that he's already more powerful than Morpheus who's presumably the most powerful of the "good guys". 

The only thing he has to do is believe in himself and he can basically beat anyone, it's pre-destined in him.

Harry Potter beats Dracoy at quiddich right away and becomes like the best little wizard in Hogwarts within a week, lol.

Gimme a break with this shit.

This is a common archetype, the messiah/Chosen One/Golden Child archetype, it's just not commonly applied to women.

The only lesson for Harry Potter/Neo is not that they needed to work hard, it's that they were already better than everyone else, they just needed to believe it. That's the character arc, like it or not.