Well, it could be that they find out some 'dark secret' about Naruto. Maybe they think he has some sort of uncontrollable power within him that they fear. Or perhaps they are forced to disown him due to political pressure in the village. There could be a group of elders or powerful clans that demand it in order to protect their own interests or maintain the so - called 'balance' in the village.
It could also be due to some external influence. Perhaps an enemy used some kind of mind - control or manipulation on Kushina. They made her think that Naruto was a threat, so she decided to disown him. In the Naruto universe, there are many powerful villains who could potentially do this kind of thing.
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.
On a more personal level, they could face internal guilt. As Naruto grows up and achieves great things on his own despite their neglect, Minato and Kushina may realize what they've missed out on. This realization could cause them a great deal of internal turmoil and regret for not being there for their son when he needed them.
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.
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.
Perhaps there was a curse or a disease that he couldn't overcome. In some fanfictions, they like to introduce unique and deadly diseases that not even the best medical ninja can cure. It could also be due to a failed mission where he was caught in a trap that was impossible to escape from, leading to his death.
If Minato and Kushina disown Naruto in fanfiction, Naruto's character might develop in a very different way. He may grow up with a sense of abandonment that shapes his entire personality. He could become extremely independent but also very lonely. His idea of family would be completely distorted. He might even start to view the concept of 'home' as something he doesn't have or need. This could also make him more empathetic towards other outcasts, as he himself has been cast out by his own parents.
Well, it could be related to Minato's absences. He was often away on important ninja business. Naruto might have felt abandoned by his father, and Kushina, seeing her son suffer in Minato's absence, could start to resent Minato. Also, there might have been some political decisions Minato made that didn't sit well with Kushina. For example, if he made an alliance that she thought was against the values of the village or their family.
One possible reason could be a misunderstanding. Maybe Naruto gets involved in some dangerous situation and they disagree on how to handle it. For example, if Naruto wants to take on a powerful enemy alone but Minato and Kushina think it's too risky.
Perhaps in this fanfiction, Naruto turns to the darker side of the ninja world. Since he lacks the love and guidance from Minato and Kushina, he might be more easily influenced by Orochimaru or other villains. He could start to believe that power is the only way to get respect and recognition, and thus embark on a path that is different from his canon self. He might also form unexpected alliances with characters who are also outcasts in the shinobi society.