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.
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.
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.
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.
Maybe Naruto hates it because Sasuke is his friend. He values their relationship and doesn't like to see Sasuke being bashed in fanfics.
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.
Maybe Naruto sees Sasuke as a strong and unique male character. Changing Sasuke into a female in fanfiction might go against his perception of their relationship and Sasuke's true identity. It could also be that he feels it's disrespectful to Sasuke's character development as a male ninja.
In some fanfics, Sakura might avoid Sasuke because she's tired of his cold and distant attitude. She wants to surround herself with people who actually care about her and value her, so she chooses to stay away from Sasuke to find more positive relationships.
She might be initially heartbroken. Sakura, being in love with Sasuke, would surely be deeply affected when he neglects her. She could become withdrawn herself, losing some of her usual cheerfulness.