One possible reason could be that Naruto has some sort of power within him that they fear. Maybe it's a power that they don't understand and think could be dangerous, so they hate him out of fear.
Well, it would likely make Naruto more withdrawn. He's already an outcast in the village, and parental hatred on top of that would deepen his sense of loneliness. He might become more distrustful of others, always expecting rejection. This could also fuel his determination in a different way. Instead of seeking recognition from the village, he might strive to prove himself just to spite his parents, if he ever found out about their supposed hatred.
Yes, there might be. Some fanfics like to subvert the expected negative situation. In these fanfics, even though the start is that Harry's parents hate him, through a series of events such as Harry showing extraordinary courage or kindness, his parents could have a change of heart. For example, he might save them from a great danger, which makes them realize their mistake and start to love him. This kind of plot twist can add more depth and surprise to the fanfic.
In these fanfics, a common theme is growth. Harry has to grow up faster and become more independent because of his parents' hatred. Another theme is the search for identity. Without the positive influence of his parents, he has to define himself. And the theme of resilience is also prominent. Harry has to be strong in the face of his parents' negative feelings and all the difficulties that come with it. He has to keep going and not let their hatred break him.
In this fanfiction, it could be that Naruto's parents were under some sort of mind - control. Some evil entity could have taken over their minds and made them feel hatred towards Naruto. Also, it might be related to a family secret or feud. There could be something in the family's past that made them believe Naruto was a stain on their family name, even though Naruto himself was innocent. It could also be a case of false information being spread around the village which made his parents believe lies about him.
One possible reason could be a curse. Maybe some enemy put a curse on Naruto's parents that made them forget about him. It could be a way to get back at them by targeting their most precious thing, which is their son.
In Naruto fanfics, Naruto's hate could be explored in various ways. Maybe it stems from the discrimination he faced as a Jinchuriki. People in the village often shunned him, which could lead to a deep - seated sense of hatred. This hatred might not be a traditional, all - consuming rage, but more of a simmering resentment towards those who made his life difficult.
In some fanfictions, Naruto might be depicted as hating his parents. However, this is a departure from the canon. In the original Naruto story, Naruto grows to understand and respect his parents as he learns about their sacrifices. But in fanfiction, authors can take creative liberties and explore different emotional states for Naruto towards his parents, such as hatred perhaps born out of feeling abandoned, even if it goes against the essence of the original story.
It could be due to a sense of abandonment. Fanfic writers might explore the idea that Harry, growing up without his parents, feels resentful. He may see other kids with their families and, in his confusion and pain, start to hate his parents for leaving him alone in the world, even though it was not their choice.