One possible scenario in such a fanfiction could be that Naruto's parents are preoccupied with their shinobi duties. They might be constantly on missions for the Hidden Leaf Village, leaving Naruto at home with caretakers who don't really pay him much attention. This could lead to Naruto feeling lonely and isolated, just as he did in the original story when he thought he had no family.
A possible plot could be that Naruto discovers that his parents' neglect is due to a secret they are keeping from him. They might be protecting him from a greater threat by staying away from him, but Naruto misinterprets it as neglect. As he digs deeper into the mystery, he uncovers the truth and has to decide whether to forgive his parents or not. This would add a lot of drama and emotional turmoil to the story.
In fanfiction, Naruto having the Rinnegan and being neglected by parents can lead to some really interesting character development. It could make him more self - reliant and distrustful at first. He might have to learn to harness the power of the Rinnegan on his own, without any parental guidance. This could result in him making some mistakes along the way but also growing stronger in unique ways.
One possible reason could be that they are too involved in their own shinobi duties. The world of ninjas is full of dangerous missions, and they might be constantly away on important tasks, leaving Naruto feeling neglected.
One possible storyline could be that Minato and Kushina help Naruto train. They could pass on their unique jutsu and combat skills directly to him. This would make Naruto even more powerful at a much faster rate compared to in the original story.
A plotline might involve Naruto starting to act out in negative ways to get his parents' attention. He could start getting into trouble at school or in the village. Maybe he would start to explore his own powers in secret, away from his family, and discover some unique abilities that he then uses to show his parents what they've been missing. Also, there could be a plotline where Naruto tries to build a relationship with his sister in secret, hoping that through her, he can get closer to his parents.
The story would be very different. Naruto's parents being alive would mean he has a support system from the start. His father could pass on his jutsu and wisdom more directly. Naruto might not have the same drive to become Hokage in the same way, as he wouldn't be seeking that family - like recognition from the village. His mother's presence would also add an element of warmth and stability to his life. And perhaps he would be more of a prodigy with both his parents' guidance, changing the power dynamics in the ninja world.
In a fanfiction where Naruto's parents are alive, they could play a major role in changing the politics of the Hidden Leaf. Minato, being a former Hokage, and Kushina with her strong Uzumaki blood, might work together to strengthen the village's defenses and relations with other villages. This would also mean Naruto doesn't have to struggle alone and could learn advanced techniques much earlier from his parents.
One plot twist could be that Naruto discovers his parents had a very good reason for their neglect, like they were protecting him from a greater danger. Another could be that the village elders knew about the neglect but did nothing, and Naruto has to confront them. Or perhaps Naruto finds out he has a secret power that was the cause of his parents' seeming neglect, as they were afraid of what he could do.
A possible plot is that Naruto is constantly bullied because of his neglected state and his unknown bloodline. As he grows, he starts to show signs of his bloodline powers, which attracts the attention of both friends and foes. His journey then becomes about controlling his powers and dealing with the past neglect of his parents while also facing the new challenges that come with his revealed bloodline.
He would be more confident. Growing up with his parents' love and presence would mean he doesn't have to constantly seek validation. So he might be less brash and more self - assured from the start.