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.
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.
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.
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.
In some fanfics, they might abandon Harry because they are under a dark spell. This spell could make them lose their love for him and force them to leave. Another reason could be that they are blackmailed by some powerful dark forces. These forces may threaten their lives if they don't abandon Harry.
One possible reason could be that in the fanfic, the author might twist the story to make it seem like his parents' actions had unforeseen consequences that affected Harry negatively. For example, their fight against Voldemort led to Harry being an orphan and having to bear a great burden from a young age.
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.
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.
Another reason could be that they had some sort of premonition or prophecy that indicated the Dursleys' place was a crucial part of Harry's future protection. Maybe a seer told them that for Harry to grow into the wizard he needs to be, he has to endure the Dursley experience first.
Another theme is the protection of the family. The parents are usually depicted as being very protective of their children. They will go to great lengths to keep Cuphead and Mugman safe from the various threats in the Cuphead world, like the Devil and his minions. This theme of protection adds a lot of drama and emotion to the fanfics.
Family values are also a big theme. They might explore how the family traditions and values instilled by the parents shape the members' characters and decisions in life. For example, stories could show how a sense of hard work and perseverance was passed down from the parents to the BTS boys.