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.
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.
It might be shown through his reactions. For example, when someone tries to touch him, he may flinch or move away quickly.
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.
In fanfiction, when Naruto's heritage is revealed during the Chunin Exams, it can have a huge impact on his relationships. His teachers, like Kakashi, might start to train him differently, realizing his true potential. His friends, such as Sakura and Shikamaru, could be more protective of him. However, some of his classmates who were jealous before might now try to isolate him. Also, ninja from other villages might approach him differently, either trying to recruit him or seeing him as a greater threat.
It could make him very distrustful at first. He might have a hard time believing that others truly care about him. For instance, when his friends try to be nice, he might think they have ulterior motives.
It would also impact his relationship with his village. The village has always seen Naruto as a part of their heritage in a way, especially considering his connection to the Fourth Hokage. If he rejects his heritage, some villagers might feel betrayed or confused.
His hatred might make him more distant from his friends. They may not understand his sudden change in attitude towards his family and this could create a rift. For example, Sasuke might be confused as Naruto was always so positive about family before.
In his relationship with his mentors, it might change the dynamic of how they guide him. Instead of using physical gestures like a hand on the shoulder for reassurance, they would have to rely more on verbal communication. This could make the bond-building process more challenging as physical touch is often a way to convey closeness and trust in these 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.
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.