The adopted sister could actually strengthen Naruto's relationships. She could bring a new dynamic to their group. Naruto would be more responsible as he has someone else to look after. His friends would see this growth in him and respect him more. They might also start to include the sister in their activities, like inviting her to training sessions or parties, which would further integrate her into their circle.
Naruto's relationship with Sasuke would be different. With a stable family life provided by Kushina, Naruto might not be as desperate for Sasuke's friendship initially. He could be more self - assured and approach Sasuke in a more balanced way. This could lead to a more positive relationship between them from the start.
It might actually strengthen his relationships in some ways. His friends could see him as an even more powerful ally. Naruto, with these new powers, could protect them better. Sakura, for instance, would feel safer around him and this could lead to a deeper bond of trust between them.
His relationship with Sasuke might be different. With Kurenai's influence, Naruto could be more understanding and patient, which might help him better deal with Sasuke's issues. His bond with Sakura could also change as he may approach her in a more mature way, having learned from Kurenai about relationships.
In fanfiction, Naruto joining Team 10 would create some interesting relationship changes. Naruto is a bit of a loner at first in the original story, but in Team 10, he could be the glue that holds them together. He has a way of making people feel important. For Ino, Naruto could be a source of inspiration in terms of becoming stronger. His presence would also add more competition among the team members, which could either strengthen or strain their relationships depending on how they handle it.
His friends might be a bit in awe at first. They are used to Naruto's ninja skills, but a Devil Fruit power would be something entirely new. They could also be a bit jealous, but mostly they would be excited to see how Naruto uses this new power in their adventures together.
Her presence could make Naruto more protective. He's already lost so much in his life, and having a sister would give him someone else to care for deeply. This might make him even more determined to become strong and protect the village, as he now has his sister to think about.
His relationships might be less intense in some ways. Since he has a family, he might not be as clingy to his friends like Sasuke. For example, he wouldn't be as desperate to bring Sasuke back because he has his parents' support at home.
Naruto's relationship with Kakashi could also change. Kakashi, being a more experienced ninja, would try to guide Naruto in using the Millennium Puzzle's power responsibly. He might teach Naruto about the potential dangers of misusing such a powerful artifact, which could bring them closer as teacher and student. Naruto's friends in Team 7 would also look to him for more leadership when they see the power the Puzzle gives him.
Naruto's dragon blood could also attract new friends or allies. There could be characters from other clans or regions who are interested in his powers and want to be associated with him. This could cause some friction among his old friends at first, but eventually they would come to accept these new relationships as long as Naruto remains true to his original friends. His relationships would become more complex and diverse, but still centered around the core values of friendship that Naruto has always held.
Naruto's relationship with his teachers could be different too. Kakashi, for example, would need to adjust his training methods for Naruto. He would have to help Naruto master the Byakugan while still maintaining his existing skills. And Naruto might also have new interactions with other powerful ninjas in the village or from other villages, as they are curious or intimidated by his new - found Byakugan - related abilities.