In the 'Banished Naruto's Parents Revealed Fanfiction', his parents could be presented as having been part of a group that was at odds with the village leadership. Maybe they were trying to bring about some kind of change that the elders didn't like. So, when Naruto was born, they were seen as a threat, and Naruto was made to suffer as a result. This would be a departure from the more heroic and straightforward view of them in the original series.
In many fanfictions, some might reveal that Naruto's parents had a more complex backstory than in the original series. Maybe they were part of a secret organization or had a special mission that led to Naruto's situation. However, without specific details about the particular fanfiction, it's hard to be more precise.
His relationship with his parents would be loving. Minato would be a strict but fair father, teaching Naruto about ninjutsu and the responsibilities of being a shinobi. Kushina would be the warm, affectionate mother, always there to comfort and encourage Naruto. They would support his dreams and be proud of his every achievement.
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.
The parents' relationship could also set an example for Naruto and Hinata. If Kushina and Hinata's mother had a strong, loving relationship, Hinata might be more inspired to be as loving and supportive in her relationship with Naruto. Similarly, Naruto could learn from his father's respect for Hinata's family and carry that forward in his relationship with Hinata.
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.
Perhaps Naruto has always felt different from others in the village. And when he finally learns about his parents, he realizes that their actions, even if they were for a good cause like protecting the village, still made his life very difficult. He might be angry that they didn't find a better way to handle things so that he didn't have to suffer so much growing up.
In this fanfiction, it could be that Naruto's parents were under some sort of mind - control. Some evil entity could have taken over their minds and made them feel hatred towards Naruto. Also, it might be related to a family secret or feud. There could be something in the family's past that made them believe Naruto was a stain on their family name, even though Naruto himself was innocent. It could also be a case of false information being spread around the village which made his parents believe lies about him.
One possible reason could be a curse. Maybe some enemy put a curse on Naruto's parents that made them forget about him. It could be a way to get back at them by targeting their most precious thing, which is their son.
In this fanfiction, the reception could be mixed. On one hand, the older generation who remembered Minato and Kushina would be very glad to see them return. They were important figures in Konoha's history. But on the other hand, some of the younger shinobi who didn't know them might be a bit cautious at first. Still, once they learn about their heroic deeds, they would likely warm up to them.