Well, if Naruto has no emotions in the fanfic, his relationships would become very strange. For example, his bond with Sasuke might not be as intense. Normally, their relationship is full of passion, rivalry, and a deep sense of friendship. But without emotions, Naruto might just see Sasuke as another ninja, not someone he has a strong emotional connection with. His interactions with Sakura would also be different. Instead of having his unrequited love for her, he'd be indifferent, which would change the whole dynamic of their trio.
In the fanfic where Naruto has no emotions, his relationships with others would be quite detached. He wouldn't be the enthusiastic and empathetic Naruto we know. His friends might find it hard to relate to him. For instance, with Iruka - who was like a father figure to Naruto - Naruto would lack the emotional response of gratitude and love. He'd probably just follow Iruka's instructions without any real emotional attachment. This would make his relationships seem more like cold transactions rather than the warm, emotional bonds in the original story.
If Naruto has no emotions in the fanfic, his relationships with other characters would be redefined. Consider his relationship with Kakashi. Usually, Naruto respects and looks up to Kakashi with a sense of admiration and a touch of hero - worship. But without emotions, that respect would be more of a mechanical recognition of Kakashi's skills. His interactions with his other friends from the village, like Shikamaru or Choji, would lack the camaraderie and shared emotions. There would be no joking around based on shared feelings, and instead, it would be more about practical matters, like mission - related stuff.
As for Kakashi, he would be in a difficult position. He has mentored Naruto and also has a strong loyalty to Konoha. He might try to understand Naruto's reasons while also having to deal with the village's reaction. Their relationship could become strained as Kakashi tries to balance his duties to the village and his connection with Naruto.
It could change his relationship with Sakura. Sakura might be a bit wary of Naruto at first because of the unknown effects of absorbing Zetsu. But as she sees that Naruto is still the same person at heart, she would gradually accept him again. With Kakashi, he might be more cautious and keep a closer eye on Naruto to make sure he doesn't lose control.
With Kakashi, Kakashi would be extremely worried. He would probably try to find a way to get Naruto out of Akatsuki without causing too much chaos. Naruto, on the other hand, would have to keep his distance from Kakashi to maintain his cover in Akatsuki, which would be a difficult situation for both of them.
His relationship with Sakura could also change. Sakura might be both amazed and a bit worried about Naruto's new power. She could see it as a great asset in protecting the village but also be concerned about Naruto getting in over his head. This could lead to her being more protective of Naruto in a different way than before, perhaps trying to study more about psychokinesis to help him control it better.
The villagers' attitude towards Naruto could also shift. Some who were always in awe of him might now pity him. But others, like the kids he used to play with, would try to make him remember the good old days. His relationship with the tailed beasts would be really interesting. If he forgets about them, they might try to communicate with him in his mind, which could be a very strange and new experience for Naruto, and it would also be a chance to explore the bond between them in a different way.
With his friends like Sakura, their relationship could shift. They might bond over more 'feminine' experiences if Naruto has a feminine body. For example, they could share stories about clothing or certain social situations that are more common among female characters. It could also lead to some jealousy or new - found respect between them.
His relationship with Sasuke would be interesting. Sasuke might be a bit confused or even annoyed at first. He's used to Naruto being his own energetic self, and now Naruto is acting like Kakashi. Sasuke might see it as Naruto trying to be something he's not. But over time, he could come to respect Naruto's new - found admiration for Kakashi and see it as Naruto growing as a ninja.
With Sasuke, Naruto's parents being alive could lead to a more positive influence on Sasuke. Naruto might be more stable and happy, and this could rub off on Sasuke. They could become closer friends earlier, and Naruto could help Sasuke deal with his family issues in a different way. Maybe Naruto's family could even offer some support to Sasuke after the Uchiha massacre didn't happen.
With Kakashi, Kakashi would probably be more protective at first. He'd be curious about how Naruto got the cat ears and would keep an eye on him to make sure it doesn't cause any harm to Naruto or the village. Naruto might feel a bit more like he has to prove himself to Kakashi that the cat ears don't make him any less of a ninja.
With Sasuke, things could get more complicated. Sasuke might see Naruto's new bloodline as another way Naruto is getting stronger while he struggles to reach his own goals. This could fuel their rivalry even more, or it could lead Sasuke to try and understand Naruto's new situation in an attempt to gain an edge himself.