In some cases, Naruto's sensory ability in fanfictions can bring him closer to his comrades. He can use it to anticipate their needs during battles, which makes them rely on him more. However, it could also make some characters jealous of his new power. They might feel that he's getting special treatment or becoming too powerful, which could strain relationships.
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 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.
It might strengthen his relationship with Sasuke. For example, Naruto could use his time - control to understand Sasuke's pain better. He could go back to the time when Sasuke's clan was massacred and truly feel what Sasuke went through, which would make Sasuke more likely to open up to him and trust him more.
Naruto's ability to see the future in fanfiction can really mess with his relationships. He could see a future where his friends die because of his actions. This would make him question his place among them and might lead to him isolating himself. With his family, like if he has a future vision about his kids, he might be overly strict or try to control their lives too much to prevent the bad things he saw from happening. And with his teacher, like Kakashi, if he sees a future where Kakashi is in danger, he may act impulsively to save him, which could cause problems in their normal teacher - student dynamic.
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 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.
It could strengthen his relationships. If Gohan has the gamer ability, he might be able to use it to protect his friends and family better. This would make them trust him more and bring them closer together. For example, he could quickly analyze a dangerous situation using his gamer skills and save his loved ones, making his relationships deeper.
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.