With his mentors or superiors, it might seem disrespectful at times. If they try to offer guidance through a touch on the shoulder or something similar, and he recoils, it could be misinterpreted. However, if they are perceptive, they could try to communicate with him in other ways to build a strong bond despite this quirk.
In a romantic relationship, it would be a major obstacle. His partner would have to be very patient and understanding. They would need to find other ways to show love and closeness, as physical touch is a common part of a romantic relationship. This could potentially slow down the development of a romantic relationship.
It might be shown through his reactions. For example, when someone tries to touch him, he may flinch or move away quickly.
Even with his mentors or senseis, his fear can be a problem. They might want to guide him physically in training, like correcting his stance by touching his arm or shoulder. But Naruto's fear could make him resist this kind of guidance, which could slow down his progress in learning new techniques.
If some of her friends don't like Naruto or Naruto fanfiction, it could cause a bit of a rift. But on the other hand, it could also be a chance for her to introduce them to the world of Naruto fanfiction and bring them around. She might also find new friends who are into Naruto fanfiction and expand her social circle.
It could make his friends more protective. Since Naruto is in a weakened state without his full chakra, his friends might be more concerned about him and try to keep him out of dangerous situations.
His relationship with Sasuke might change. Sasuke always saw Naruto as a strong rival, and a big part of Naruto's strength was Kurama. Without Kurama, Sasuke might view Naruto differently. Also, Naruto's friends might be more protective of him, as they know he's lost a major source of power.
On the positive side, it could bring him closer to those who also have issues with his father or the old ways. There might be some characters who have been wronged by Naruto's father's decisions in the past. Naruto's hatred could make them form an alliance of sorts, united by their shared negative feelings. However, overall, it would likely cause more problems than benefits in his relationships.
On one hand, it can strengthen his relationships. His friends might be inspired by his seemingly unwavering happiness. They might think that Naruto is so strong - mentally and emotionally - that they admire him more. For example, Sakura might see his happy face and feel more confident in their team.
Maybe it's related to his sense of independence. Naruto is used to relying on himself and having others touch him might make him feel like his personal space and autonomy are being invaded. He's always been on a journey to prove himself, and being touched could be seen as a form of interference in that self - discovery process.
With his friends like Sakura, they might be worried about him. Sakura could try to reach out to Naruto, but if he's snapped, he might push her away. This could create a rift in their friendship. On the other hand, some of his other friends might be inspired to help him get back on track, understanding that he's under a lot of pressure.
His prototype powers could make others either fear or envy him. Some might see him as a threat due to his new and untested abilities. For example, villagers who were already suspicious of Naruto because of the Nine - Tailed Fox might be even more wary.