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.
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.
It could also affect his friendships. Some friends might try to convince him to let go of his hatred, which could cause friction. On the other hand, some friends might support his stance, which could lead to them being at odds with the clan. For example, Sasuke, who has his own issues with his clan, might react in different ways depending on Naruto's situation.
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.
Well, it might make him more withdrawn from his friends. If he hates his family, he might be less trusting of others in general. So, his friendships could become strained as he struggles to open up to them.
His relationship with clan members might become strained. They may side with their clan heads, causing Naruto to be at odds with them even if he was friends with some of them before. For instance, if a clan member is loyal to their head's views that Naruto opposes.
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.
Well, it really depends on how the fanfiction portrays it. If Naruto absorbs his dark emotions in a way that makes him seem cold or emotionless, it could strain his relationships. His friends are used to his passionate and sometimes impulsive self. But if he manages to balance it well, it could also make him a better listener and friend. He'd be able to offer more rational advice and support without being clouded by his own negative feelings.
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.
It might make him more distant from his friends at first. He could be so consumed by his anger towards his parents that he withdraws from his usual social circle. For example, he might avoid spending time with Sasuke or Sakura because he is too preoccupied with his feelings about his parents.