He could form relationships with other outcasts. People who also don't have a home or a place in society. They could band together and form a sort of 'family' of misfits.
Well, he could form new relationships with people from different villages. Since he doesn't have the ties of a home village, he's more likely to roam around. He might meet some friendly ninjas from other places who take pity on him or see his potential. These new relationships could be based on mutual respect for his skills rather than his origin or family name. And he could also form relationships with people who have unique powers or abilities that he can learn from, which would be different from the relationships he had in his home village.
He could develop some sort of psychic power that doesn't rely on chakra. This could be a power related to his willpower, allowing him to influence the minds of his opponents or sense their intentions from a distance.
He might form more protective relationships. His friends would be more likely to look out for him. For example, Sasuke might be more hesitant to leave the village knowing Naruto is in a more vulnerable state.
Well, not having a home in a fanfiction could make Naruto more independent. He'd have to rely solely on himself more. Maybe he'd become more distrustful of others at first because he has no safe place to call home. He'd be constantly on the move, which could make him a better fighter as he'd learn different survival skills.
He could form some really interesting relationships. He might befriend the underdogs, like the Starks, and use his powers to help them. Or he could have a mentor - like relationship with someone like Tyrion, sharing his wisdom from his own world. He could also have an adversarial relationship with the more power - hungry characters, like Cersei, as his values would likely clash with hers.
Naruto could attract the attention of other villages' ninjas who are interested in his unique power. This could lead to new alliances or rivalries. Some might want to learn from him, while others might see him as a threat. So, new diplomatic relationships could be formed based on how other villages react to his all - elemental - affinity power.
He might form closer bonds with local heroes in his neighborhood. Since he's not at UA, he would have more time to interact with the heroes who operate near his home. They could become his mentors or friends, guiding him in his hero journey.
He could form a mentor - like relationship with some of the younger characters in High School DxD. His experience and power could help them grow. Also, he might have an uneasy alliance with the devils, as they could be interested in his power. Maybe a friendly rivalry with some of the more powerful angels.
Regarding his relationship with the villagers, Naruto might face some discrimination at first. People are often afraid of the unknown, and his new bloodline abilities from Zetsu could make them uneasy. However, as Naruto continues to use these powers for the good of the village, they would gradually accept him. His friends from the Hidden Leaf, like Shikamaru and Choji, would be curious about his new abilities. They might work together with Naruto to develop new strategies in battles, leveraging Naruto's Zetsu - like powers.
One possibility could be that Naruto discovers some ancient and long - forgotten ninja techniques. These techniques might give him powers similar to or even more powerful than the Kyuubi's. For example, he could find a scroll that teaches him how to manipulate natural energy in a unique way that no one has ever done before.
Maybe they don't like fanfiction in general. It could be that they prefer the official, canon Naruto story. Fanfiction can vary greatly in quality, and they might have had bad experiences with some poorly written Naruto fanfictions in the past, which made them dislike the whole concept of Naruto fanfiction.