Maybe Karin has some personal reasons. For example, she might not like Sakura's character in the original work, so she also dislikes fanfic related to Sakura.
There could be a conflict between Karin and Sakura in the original story that makes Karin not want to see any fan - made stories about Sakura. This dislike then extends to Sakura fanfic.
Well, it could be that in certain fanfics, the writers want to create a more complex and angsty story. Sasuke's character is often seen as a brooding and driven one. So, they make him hate Sakura perhaps because they think it adds an interesting dynamic. For example, if Sakura is constantly trying to get close to him but he hates her, it can lead to a lot of conflict and emotional turmoil in the story.
Maybe in the fanfic, Itachi has done something that goes against Sakura's beliefs or values. For example, he might have made a decision that put her friends in danger.
Well, in fanfic, the writer can take creative liberties. It could be that Naruto has grown and evolved in a different way than in the original story. He might have seen Sakura's flaws more clearly over time. For example, her obsession with Sasuke could be seen as a negative trait that affects the team dynamic. And as Naruto values the team highly, this could cause him to develop a dislike and eventually hate for Sakura.
In fanfiction, Naruto could hate Sakura due to her treatment of him. She often overlooked his feelings in the original series. Fanfic authors might exaggerate this aspect. For example, if Sakura continuously dismisses Naruto's achievements or makes him feel inferior, it can build up to a strong dislike or hatred in the fan - created stories. Also, some fanfictions might explore a darker side of Naruto where his pent - up emotions turn into hatred for Sakura, perhaps as a way to show his growth into a more complex character with a wider range of emotions than just the positive ones shown in the original anime.
Another reason could be that she values the authenticity of the original Naruto narrative. Fanfictions are often the product of fans' wild imaginations and might not align with the official story. She might be a purist when it comes to the Naruto story she is a part of, and thus hates fanfiction that strays too far from the original.
In some fanfiction, Sakura might hate Sasuke because of his actions towards her. For example, he may have continuously rejected her advances coldly. This could lead to her developing feelings of hatred as her love is not reciprocated and instead met with indifference or rudeness.
In some cases, Karin can be more popular. Her backstory of being associated with Orochimaru and her survival instincts make her an appealing character. Some fans might be drawn to the idea of her as an underdog in the love triangle with Sasuke and Sakura. Also, her sensing abilities and her role in certain plot points in the original series can be explored more deeply in fanfics, which might make her more interesting to some readers than Sakura.
Often, it starts with the establishment of their dislike. Then, there could be a series of confrontations. For instance, they might argue or compete in some way, like in a ninja mission where they constantly try to outdo each other.
Karin could be heartbroken. She might initially be angry and feel betrayed, lashing out at Sasuke for choosing Sakura over her.
In some fanfics, Bucky might be written to hate Steve due to misinterpretations or plot twists. Maybe the writer wants to explore a darker, more conflict - ridden relationship. It could be that Bucky has been brainwashed in the fanfic and his altered mind now sees Steve as an enemy, or there could be some past event that was misconstrued and led to this hatred.