In terms of his relationships with the wider village, his hatred for his clan could be misinterpreted. People might think he is being ungrateful or causing trouble. This could lead to some villagers distancing themselves from him, while others might try to get involved to either support him or change his mind, depending on their own views and relationships with the clan.
It could also affect his friendships. Some friends might try to convince him to let go of his hatred, which could cause friction. On the other hand, some friends might support his stance, which could lead to them being at odds with the clan. For example, Sasuke, who has his own issues with his clan, might react in different ways depending on Naruto's situation.
His relationship with Sasuke could be affected in a big way. Sasuke is very much tied to his clan, and Naruto's rejection might make Sasuke view him differently. It could either create a rift between them or make Sasuke question his own loyalty to his clan. As for his friends like Sakura, she might be initially shocked but then try to understand Naruto's perspective.
His relationship with clan members might become strained. They may side with their clan heads, causing Naruto to be at odds with them even if he was friends with some of them before. For instance, if a clan member is loyal to their head's views that Naruto opposes.
Perhaps there were some dark secrets in his clan that he discovers. These secrets could be related to past wrongdoings, like how they treated other clans or individuals. If Naruto has a strong sense of justice, learning about these things might make him hate his clan. It could also be that he feels ostracized or different within his clan, like if he has abilities or beliefs that are not accepted by the majority of the clan members.
Some friends might feel betrayed. If they are very clan - oriented, they could see Naruto's leaving as a sign that he doesn't value the clan and by extension, their friendship. However, his true friends like Sasuke or Sakura might understand his reasons. Sasuke, who has his own issues with his clan, might be more empathetic. Sakura, who has seen Naruto's determination, could support his decision in the long run.
His hatred might make his relationships with his friends more complicated. For instance, Sasuke might view Naruto's hatred in a different way, either sympathizing with him or trying to convince him to let go of the hatred. This could create some tension or deeper understanding between them.
Well, it might make him more withdrawn from his friends. If he hates his family, he might be less trusting of others in general. So, his friendships could become strained as he struggles to open up to them.
Well, in some fanfictions, Naruto might start by finding suitable partners within the village. Since he is the last of his clan, he could look for women who are willing to carry on the Uzumaki bloodline. He may also use his influence as a hero to encourage others to support his clan - revival efforts, like getting the village to provide resources for the new Uzumaki generation.
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 some fanfictions, Naruto might restore his clan by using a powerful jutsu to bring back the dead members. For example, a fictional super - level resurrection jutsu could be discovered. However, this would likely have many consequences and moral implications within the Naruto universe.
His relationship with Sasuke would be different. Without the same rivalry born from being in the same class at the Ninja Academy, their bond might be more of a friendly one from the start. Naruto might be more composed around Sasuke, as the Hyuuga upbringing would have instilled more discipline in him.