It can create misunderstandings. For instance, his friends might think he doesn't like them if he recoils from their touches. His romantic relationships could also be affected. If he's in love with someone in the fanfiction, his fear of touch would make it difficult for him to show physical affection, which is an important part of a romantic relationship.
It can make his relationships more intense. For example, in his friendships, he might be overly eager for hugs or physical contact from his friends like Sasuke or Sakura. This could initially surprise them but then lead to a deeper bond as they understand his need. In romantic relationships in the fanfiction, his touch - starved nature might make him more clingy at first, but also very loving and devoted once he feels secure in the 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.
With Sasuke, it could either drive a wedge or bring them closer. If Sasuke blames himself for Naruto getting injured while protecting him, he might distance himself out of guilt. On the other hand, it could also make Sasuke realize how much Naruto means to him and he could become more committed to their friendship.
His apathy can strain his relationships. His friends might feel neglected. For instance, Sakura could be confused and hurt as Naruto no longer shows the same eagerness to be part of the team.
The fear could also make him question his own identity as a ninja. If he is afraid of ninjas, does that mean he is also afraid of what he is? This internal conflict would be a major part of his character development. He would have to face his fear, understand the true nature of being a ninja, and decide whether he wants to continue on the ninja path or find an alternative way of life.
His illiteracy might make his friends initially frustrated. For instance, Sasuke, who is more studious, could be impatient with Naruto's inability to read important messages. But as they grow, they might become more understanding.
It could make some relationships stronger. His friends might be in awe of his new powers and look up to him even more. But it could also create some distance, as his new status might make others feel inferior.
His friends might start to avoid him. If Naruto is constantly snapping at them, they'll feel hurt and not want to be around him as much.
The Uzumaki bloodline can also affect his relationships with characters from other villages. In fanfiction, ninja from other villages who know about the Uzumaki's power might either fear or respect Naruto more. This could lead to different diplomatic situations. For example, a village might be more willing to negotiate with the Hidden Leaf because of Naruto's Uzumaki bloodline. On the personal level, he might meet other Uzumaki descendants in other villages, and they could form a strong bond based on their shared bloodline.
His depression could strain his relationships with his friends. They might not understand why he has become so withdrawn and moody. For instance, Sakura might try to reach out to him, but Naruto could push her away, causing a rift in their friendship.