The whole team dynamic could be affected. If Sasuke is also there, he might react in a certain way. He could side with Naruto, thinking Sakura was being too much, or he could defend Sakura. This would then change the way the three of them interact for the rest of the fanfiction story.
It could be that in the context of the fanfiction, there is a lot of tension. Naruto might be in a hurry or in a very serious situation, and Sakura's chatter is getting in the way. For example, if they are in the middle of a battle plan or facing an immediate threat, Naruto needs everyone to be focused, and Sakura's talking is a distraction, so he tells her to shut up.
In the movie Dune 2, the Virgin Helen said the word "Abomination", and the subtitles translated it to "Shut up". However, this translation did not match the character's identity and setting. In fact," Abomination " was a proper term in the original novel. It was usually used by the Bene Gesserit Sisters for those who drank the Life Potion and were unable to…Therefore, we can conclude that in the movie Dune 2," shut up " is not the correct translation.
Sakura's obsession with Sasuke. Naruto might be fed up with how Sakura always puts Sasuke first, ignoring the people around her who truly care about her, like Naruto himself. So he tells her off to make her realize her wrong priorities.
He may try to talk to Sakura and understand her reasons. Naruto is a character who believes in the goodness of people. So, instead of getting angry immediately, he would likely want to resolve the issue. He could also become determined to prove himself to Sakura, that whatever she thinks he has done wrong, he is actually not that person.
Sometimes, in fanfiction, Naruto stands up to Sakura when it comes to her attitude towards Sasuke. Sakura might be blindly following Sasuke's every move, and Naruto, having a more objective view of Sasuke, could confront Sakura. He would tell her that she should value herself more and not just revolve her life around Sasuke. Naruto has his own understanding of friendship and loyalty, and he would use that to make Sakura see things differently.
In this case, Sakura could be seen as the antagonist, at least in that particular moment when Naruto tells her off. Since Naruto is the one doing the telling - off, it's because of something Sakura has done or said that has pushed him to that point.
Well, it could be that Sakura makes a really bad decision during a mission, like endangering the whole team because she was being too overconfident. Naruto, who has grown tired of her reckless behavior, tells her off. He might say things like 'Sakura, you can't keep acting this way. You're putting all of us at risk!'
One possible plot could be that Naruto has finally had enough of Sakura's constant nagging or her one - sided focus on Sasuke. So he tells her off in a moment of exasperation, perhaps pointing out how she's been neglecting their friendship or the team spirit in pursuit of Sasuke.
Maybe in the fanfiction, Molly was being overbearing. Harry might have been frustrated with her constant interference or mothering in a particular situation.