Well, it could really mess things up. Naruto's relationships are often based on his big heart and passion. If he seals his emotions, his interactions would become more mechanical. People who love him for his energy, like Iruka, would find it hard to connect with this new, emotionless Naruto. He'd be like a different person, and his relationships would have to start from scratch in a way.
In the fanfiction where Naruto seals his emotions, his relationships would be drastically altered. His bond with his friends has been built on mutual understanding and shared emotions. Without those emotions, he may not respond to their concerns or joys in the same way. His enemies might also be thrown off, as they're used to his fiery and emotional reactions. This change could isolate Naruto from those he cares about, and he might have to relearn how to interact with people on a more detached level.
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.
His relationships would be in turmoil. Naruto not being aware of his emotions is like sailing a ship without a compass. In his relationships, especially with those close to him, he'd be lost. He might do things that seem out of character because he's not in touch with his feelings. For instance, when it comes to his sensei, he may not be able to show the proper respect or gratitude because he doesn't understand the emotions behind those concepts. His friends would constantly be trying to figure out what's wrong with him, and he'd be equally confused, leading to a lot of strife in his relationships.
Well, he would probably become much more cold and detached. He might lose his drive to protect his friends and the village in the same passionate way. His actions would be more mechanical, lacking the warmth and empathy that used to be his trademarks.
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.
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 where Naruto is a wolf, his relationships can change significantly. For instance, his friendship with Sasuke might be more of a rivalry based on their different natures, with Sasuke seeing Naruto's wolf - like wildness as a threat. His relationship with Sakura could also be different. She might be more cautious around him at first, but as she gets to know his true self, she grows to accept his wolf side.
Well, it could strengthen his bond with some characters. For example, he might feel a closer connection to his clan members if he discovers his heritage. He could also gain new respect from his peers who now see him in a different light, perhaps as a more important figure within the village due to his lineage.
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.
Since Naruto is quiet, he may not be as quick to make friends as in the original story. But the friends he does make could be more special. They would likely have to make an effort to get to know him better. His quietness could also make his friends more protective of him in a sense. They might see him as more vulnerable, and so they'll be there to stand up for him when needed. And as he gradually opens up to them, it could create a very deep and meaningful friendship that's based on a true understanding of each other.
His relationship with his sensei, like Kakashi, could also be affected. Kakashi might be more inclined to share certain knowledge or secrets with Naruto if the glasses are a sign of a new level of maturity or understanding. And Naruto could look up to Kakashi even more as he tries to figure out how to best use whatever advantage the glasses give him.