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.
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.
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.
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.
In many Naruto fanfictions where Naruto meets Kushina and Minato, it often creates a very emotional scenario. Naruto finally gets to meet his parents who he has only heard about. It could be a heart - warming reunion where they share stories, hugs, and Minato and Kushina get to see how far Naruto has come.
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.
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.
Many fanfictions show their relationship as one of mutual respect and admiration. Minato is often portrayed as being attracted to Kushina's strong will and red - hot hair, which is a symbol of her fiery personality. They start as friends, training together and gradually realizing their feelings for each other.
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.
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.