The fanfiction could develop this hatred through the introduction of new characters. These characters might feed Naruto false information about Minato and Kushina, making him question their motives and ultimately hate them. For example, a character who has a grudge against the Uzumaki family could manipulate Naruto.
Perhaps in this fanfiction, there is some sort of misinformation. For example, someone has spread false rumors about Naruto being a threat to the village, and Minato and Kushina believe it without proper investigation. This could lead to their hatred.
At first, Naruto and Kushina might start to distance themselves from Minato. They could avoid him and not talk to him as much. As time goes on, the hatred might grow deeper. Naruto could start to oppose Minato in public or in important village matters. Kushina might also try to influence others in the village against Minato.
One possible reason could be a misunderstanding. Maybe some false information was spread about his parents that made Naruto believe they were bad. For example, if there were rumors that Minato sacrificed the village for some other purpose rather than to save it, Naruto might be angry at him.
This fanfiction could also change the relationships with other characters. For example, if Kushina hates Minato, the Third Hokage might have to step in more often to mediate between them. And the other villagers might also take sides, creating a divided village atmosphere that is quite different from the united one in the original story.
The plot could develop as Naruto tries to expose Ozpin's secrets. He might gather evidence against Ozpin and try to convince the RWBY characters of Ozpin's wrongdoings. This would create a lot of tension and conflict within the story.
Well, in the original story, Naruto idolizes his parents. But in this fanfiction, the hatred is a complete deviation. It changes Naruto's character motivation entirely. Instead of being driven by a desire to live up to his parents' legacies, he's now driven by this negative emotion towards them.
The original Naruto story is built on themes of love, sacrifice, and the pursuit of dreams. When you have a fanfiction where Minato and Kushina hate Naruto, it undermines these themes. For example, Minato's sacrifice in the original was for Naruto's future. But in this fanfiction, that meaning is lost as they are now against Naruto. It's a huge deviation from the positive and motivational elements of the original story.
It might be due to jealousy. If Minato was getting more attention or praise in the village for his achievements while Kushina felt overlooked, that could create resentment. Say, Minato was constantly being hailed as a hero for his speed and battle tactics, and Kushina, who also had great power, felt like she was in his shadow.
Naruto's character development in such a fanfiction would likely be very different from the original. He may become more withdrawn at first, hiding his pain of being ignored. But as time goes on, he could develop a stronger sense of self - reliance. Since he doesn't have his parents' support, he has to figure things out on his own. This might make him a more independent and resourceful ninja in the long run.
Often, it portrays Dark Naruto as extremely bitter. He may be shown constantly thinking about Kushina in a negative light, with his every action towards her being full of malice. For example, he might plot revenge against her, even though she is dead in the original story.