The relationship could also affect the power balance. Naruto and Madara together would be an extremely powerful force. Other villages might view this union with suspicion or try to form alliances with them. This would lead to a shift in the political and power dynamics of the Naruto world, with different villages realigning their strategies based on this new brotherly relationship.
Their relationship would likely shift from being enemies to something more complex. Naruto's help might make Madara view him as an equal or even a friend. Madara, who has been alone in his ideology for so long, might start to respect Naruto's different perspective on peace.
The plot would change drastically. For one, the Uchiha massacre might not have happened as Naruto could have influenced Madara to prevent it. Also, Naruto would have had access to Uchiha knowledge and techniques from a young age. This would make him even more powerful. And his relationship with Sasuke would be more complex as they would be related through Madara.
The storyline would change drastically. Instead of following the path of protecting Konoha, Naruto would be involved in Akatsuki's missions. These missions are often related to capturing tailed beasts, which is the opposite of what he has been doing. So, there would be a complete reversal of his goals.
In this fanfiction scenario, Naruto being Mito's brother would likely impact the political landscape too. The Uzumaki clan has always had an important role, and with this new relationship, Naruto could have more influence in diplomatic matters. Maybe he would have been more involved in the affairs of the Hidden Leaf earlier. Also, his relationship with the other clans, especially those related to the tailed beasts, might be different. For example, his connection with the Uchiha clan could be altered as he has this new Uzumaki - related status.
The original Naruto story would be turned upside down. Naruto being Hinata's twin would affect his relationship with Sasuke too. Maybe instead of his intense rivalry with Sasuke, Naruto would focus more on family matters. His dreams might also change as he would be part of the Hyuga clan. The Hyuga clan's secrets and techniques could be shared with Naruto more easily. This would give him an edge in battles and change how he approaches his ninja career. His friends like Shikamaru and Kiba might view him differently as well, since he would now be associated with the Hyuga clan rather than just being the orphaned Uzumaki.
At first, it might be very rocky. Naruto would be suspicious of Madara given his reputation. But as time goes on, if Madara shows genuine care and teaches Naruto useful skills, Naruto could start to respect him. Eventually, they could develop a father - son - like bond.
There could be a shift from enmity to a begrudging respect. Madara has always been a powerful and feared foe, but with Naruto being stronger, Madara may have to accept Naruto's superiority. Naruto, on the other hand, would likely try to understand Madara's motives better and might try to reform him rather than just defeat him.
The story would change drastically. Naruto's identity as a descendant of Madara would immediately put him at odds with some in the village who still fear the Uchiha. His journey to become Hokage would be even more challenging as he has to prove that he's not going to follow in Madara's footsteps. Also, his training might take a different route. He could be taught some ancient Uchiha techniques by an unexpected mentor, perhaps an old Uchiha who has been in hiding.
His combat abilities would become more diverse. Madara could teach him new forms of taijutsu and ninjutsu. For example, Naruto might learn some of Madara's signature space - time ninjutsu, which would give him an edge in battles. His chakra control would also improve as Madara is very proficient in chakra manipulation.
The Akatsuki might take advantage of the chaos. With the village in disarray due to Sakura's death, they could launch more attacks. The balance of power in the Naruto world would be disrupted. The other villages might also see this as an opportunity to gain an edge over Konoha.