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.
It could also lead to some division among the Naruto fandom. Those who support Sakura's view might be more critical of fanfiction, while those who love fanfiction might not like Sakura as much because of her stance. For example, in online Naruto communities, there could be debates and arguments about whether Sakura is right to hate fanfiction.
Naruto might become more determined. He's the type who turns negative things into positive motivation. So, Sakura's meanness could make him strive harder to prove himself.
In a fanfiction where Sakura cheats on Sasuke with Naruto, there could be many consequences. Firstly, it would shatter the trust within Team 7. The camaraderie and unity that they had built over the years would be severely damaged. For Sakura, she might lose the respect of her friends and comrades. In the Naruto world, reputation is important. Naruto himself might be ostracized by some in the village who see him as a home - wrecker, despite his good intentions. And Sasuke could potentially go on a dark path again, seeking revenge or just distancing himself from everyone. Overall, it would create a lot of chaos and emotional upheaval.
Naruto could be forced to wear an embarrassing outfit for a day. Maybe something like a pink frilly dress, much to his dismay, and Sakura would get a good laugh out of it. He would be the talk of the village for that day.
One possible consequence could be a major shift in the relationships within the 'Naruto' world. It would create a huge rift between Naruto, Sasuke, and their respective friends. There would also be a lot of drama regarding family and clan issues, especially considering Hinata's and Sakura's family backgrounds.
It might also cause Naruto to lose control more easily. If he hears such a hurtful term from someone he cares about like Sakura, it could make him more vulnerable to the Nine - Tails' influence. In the long run, it could be a turning point in his character development, either making him more bitter or more determined to show everyone, including Sakura, that he's not what she says.
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.
Maybe in the fanfiction, Molly was being overbearing. Harry might have been frustrated with her constant interference or mothering in a particular situation.
One consequence could be that Sakura feels rejected and this might lead to her character developing in a different way. She could become more independent or focus more on her own skills. Another consequence is that it could change the dynamic of their friendship group. If Naruto and Sakura are not interacting, it might affect how other characters interact with them too.