Naruto could be found by Orochimaru. This would be a very dark turn. Orochimaru could use Naruto's potential for his own evil plans. Naruto would be trained in Orochimaru's unethical ways, and his view of the ninja world would be completely distorted. He might become a villain or at least an anti - hero, very different from the Naruto we know in the original story.
Perhaps it has to do with a prophecy. They might think that Naruto has a special destiny and that their leaving is a necessary step to set that destiny in motion. They could believe that Naruto needs to grow up on his own to become strong enough to face future challenges.
In some cases, Naruto might initially become bitter towards his parents. But as he experiences more in life and learns about the possible reasons behind their actions, he could come to understand and even forgive them. His reaction would also depend on the people around him. If he has good friends or mentors, they could help him deal with his emotions in a more positive way.
The story could also show Naruto being taken in by other characters, like Iruka at a very early age. Iruka, seeing Naruto's situation, decides to be like a father figure to him. Naruto might then develop a different set of values based on Iruka's teachings rather than the absent influence of Minato and Kushina. He could become more focused on family values within the village, seeing the village as his true family since his biological family left him.
Even Kakashi could be a role model for Naruto. Kakashi has his own traumas and has learned to deal with them. He could show Naruto how to be strong in the face of difficulties and how to use his skills for the good of the village. Kakashi's sense of loyalty and duty could inspire Naruto to be a great ninja despite his difficult start in life.
If Minato and Kushina abandon Naruto in a fanfic, it could lead to a much darker Naruto. He might grow up more jaded and bitter. Without their love and support, he could be more easily influenced by negative forces. Maybe he'd have a harder time believing in friendship and loyalty, which are such important themes in the original story.
One possible reason could be some sort of dark influence or curse that makes her lose her maternal instincts. Maybe a powerful enemy targets her and in order to protect Naruto from further danger related to her, she feels forced to abandon him. Another reason might be that she is made to believe false information about Naruto, such as that he will bring great disaster to the village in the future.
One possibility could be that Naruto discovers a long - hidden secret about his family that makes him feel betrayed. For example, he might find out that Minato and Kushina had made a deal with a dangerous enemy in the past that put the village at risk. This would be so against Naruto's values of protecting the village and his friends that he decides to leave them.
Maybe in the fanfiction, there is a powerful enemy who wants to use Naruto's connection to his parents against him. So, they somehow manage to bring Minato and Kushina back to the physical world. When they meet Naruto, it's an emotional moment. They form a plan to defeat the enemy together. Minato uses his strategic skills, Kushina her strength, and Naruto his own unique abilities learned over the years.
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.
Maybe she was forced to for some dark reason. Perhaps there was a threat to Naruto's life if she stayed, and she thought leaving was the only way to protect him.