Well, if Naruto is emotionless in this fanfic, his relationship with Sasuke would be drastically different. There would be no intense rivalry based on emotions like in the original Naruto. In the Bleach world, his relationship with Ichigo might be more of a power - centered one. Since Naruto doesn't feel emotions, he might only see Ichigo as a means to an end, like a source of power or a tool to achieve his goals in this new crossover world.
For Naruto's relationships in the Bleach part of the fanfic, his interaction with Orihime would be strange. Orihime, being a very emotional and kind - hearted person, would be confused by Naruto's lack of emotions. Naruto might not understand Orihime's selfless acts and would just view her as an oddity. With Uryu, Naruto could have a more detached relationship. They might work together on some tasks because of their respective powers, but there would be no real emotional bond between them.
In the context of the Soul Society, Naruto's relationship with the captains would be unique. Captain Hitsugaya, for example, who is usually strict and values order, would find Naruto's emotionless state both a challenge and a mystery. Naruto wouldn't be intimidated by the captains' authority as he doesn't have the normal emotional responses. His relationship with Rukia could be more of a student - teacher type in a way, but without the emotional undertones of a normal friendship. Naruto would simply learn from Rukia about the ways of the Soul Society without forming any emotional attachment to her.
Well, if Naruto were an emotionless ANBU in a Bleach fanfiction, he might be a really efficient fighter. He'd probably approach battles in a very cold and calculated way, like how ANBU are supposed to be. Maybe he'd cross paths with some Bleach characters and they'd be quite shocked by his lack of emotion. For example, Ichigo might initially mistake him for an enemy with his stoic demeanor.
With Kakashi, Naruto's lack of emotions would mean he no longer has the same student - teacher bond. Kakashi is used to Naruto's determination and exuberance. Without emotions, Naruto would be like a different person. He'd follow Kakashi's orders mechanically without the usual eagerness and the relationship would become more of a cold, professional one.
His relationship with Sasuke would become very strained. Usually, they have a complex bond based on rivalry and friendship, but as an emotionless killer, Naruto would see Sasuke more as a target or an obstacle. He wouldn't care about Sasuke's own goals or feelings.
He could be a sort of enigma. His role might be that of a lone wolf, going on solo missions that require stealth and quick decision - making without the interference of emotions. For instance, he could be sent to infiltrate a group of Hollows or a rogue Soul Reaper faction.
The relationships would change drastically. Naruto, known for his positive and friendly nature, would likely try to befriend many Bleach characters. For example, he might form a close bond with Ichigo as they both have a strong sense of justice. However, some characters from Bleach might be initially suspicious of Naruto's strange powers. In the same vein, Bleach characters might introduce Naruto to new concepts like the importance of reiatsu, which could change how he views power. And relationships within each universe might also shift as characters from one series interact with those from the other.
Naruto would probably befriend Ichigo right away. They both have a strong sense of justice and a desire to protect their friends. Sasuke, on the other hand, might be more aloof at first. He could be intrigued by Urahara Kisuke's mysterious nature. Naruto would likely get along well with Orihime too, as she has a kind heart. Sasuke might have a more competitive relationship with Byakuya, seeing his power and discipline.
With his Anbu comrades, Naruto's emotionless state would create a sense of distance. They would find it hard to trust someone who doesn't show any emotions. However, some might respect his cold - efficient way of handling missions. In the long run, if he doesn't change, he might be isolated within the Anbu ranks, as relationships in the Anbu are also based on some level of mutual understanding and emotional connection.
With his friends like Grover, Percy would seem like a completely different person. Grover is used to Percy's emotions guiding his actions. Now, Percy would be cold and calculating. His friends would have to constantly remind themselves that this is still Percy, but it would be hard for them to connect on the same level. They might start to doubt if they can still trust him, as his lack of emotions could make his decisions seem unpredictable.
His relationships take a big hit. His friends like Sakura and Shikamaru would find it hard to connect with him. Sakura, who's used to Naruto's warm and often goofy self, would be at a loss. Naruto's lack of emotion means he won't show the same level of care or enthusiasm towards her. With Shikamaru, their conversations would be very different. Shikamaru is used to Naruto's emotional outbursts and quick decisions based on feelings. Now, Naruto would be more reserved and logical, which could strain their friendship.
His relationship with Sasuke would be very different. Since Naruto is raised by ANBU, he might be more competitive with Sasuke in a cold, calculating way. Instead of the friendly rivalry in the original, it could be a more intense battle of skills. Naruto might not be as open to befriending Sasuke, seeing him as a potential threat to his own goals and the secrets he has been taught by the ANBU.