One consequence could be that Naruto becomes an outcast in a different way. In the original, he was an outcast because of the Nine - Tails, but here, it could be because of his abandonment. He might not have the same dreams of becoming Hokage. Instead, he could be more focused on survival.
The consequences would be huge. Naruto would lack the emotional support and guidance that Minato and Kushina would have provided. This could make him more vulnerable to the influence of Orochimaru or other villains. Also, the village's attitude towards him might be even more negative, seeing him as a reject not only of the village but also of his own parents.
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.
The village of Konoha would also be affected. With Minato still alive, he could continue to lead the village and make different decisions. This might change the relationships between Konoha and other villages. For example, there could be more peaceful alliances as Minato is known for his diplomatic skills. Also, Kushina being alive would mean that the Uzumaki clan might have a stronger presence in the village, which could lead to new jutsu developments and a different power balance within Konoha.
One consequence could be a shift in Naruto's character development. Having his mother back might make him more at ease and less driven by his past loneliness. It could also change his relationship with other characters. For example, his bond with his father figure, like Iruka or Jiraiya, might not be as strong as it was when he was motherless. Another consequence could be in the political aspect of the ninja world. Kushina was an Uzumaki, and her return could strengthen the Uzumaki clan's position and influence, which might cause some unrest among other clans who fear the growing power of the Uzumakis.
If Kushina and Minato abandoned Naruto in fanfiction, it would completely change the Naruto's character development. Naruto grew up lonely and seeking recognition because he was an orphan. Without their abandonment, he might have had a very different personality, perhaps more confident from the start. Also, the relationships in the village would be different. For example, Iruka might not have had the same special bond with Naruto as he did in the original story.
There's a fanfic called 'Minato's Return'. In this story, Minato somehow returns and gets to see Naruto's growth. It's really interesting to see how he interacts with Kushina, who is also there in the story, and how they both guide Naruto in new ways. The descriptions of their family bond are heartwarming.
Well, if Naruto was raised by Minato and Kushina, one major change would be his self - esteem. He wouldn't be the outcast he was in the original story. Growing up with his parents, he'd have a strong sense of family and love. He'd probably be more confident in his abilities from the start. Also, his training might be different. Minato could teach him some of his signature jutsu at an earlier age. And Kushina could pass on her strong - willed nature to him more directly.
Well, in a typical scenario for this kind of fanfic, Kushina might have left Naruto due to some difficult situation or misinformation. When she discovers Naruto has become 'godlike', perhaps with extraordinary powers and a great reputation. Her regret could lead to her attempting to reconnect with Naruto. She may face obstacles like Naruto's initial resentment or the complex political and social situations in the Naruto world that prevent a smooth reunion.
Minato would probably be very proud. He might notice Naruto's use of his own jutsu and be impressed by how Naruto has developed his skills. Kushina would be more emotional, maybe crying at the sight of Naruto growing up so well.
In a fanfic, Kushina might be depicted as a source of great wisdom for Naruto. Since she was his mother, she could pass on some Uzumaki family secrets or just some motherly advice. Minato could be the guiding force in Naruto's development as a ninja. His skills and experiences could be something that Naruto looks up to. Naruto himself should be a complex character, with his own insecurities and doubts at times, but always pushing forward because of his parents' influence.
The story would change a great deal. For one, Naruto wouldn't have the same connection to the Nine - Tails as he does in the original. Minato sealed the Nine - Tails into Naruto, so without that relation, the whole dynamic of the Nine - Tails within Naruto would be different. He might not have the same power - up moments related to the Nine - Tails.