At first, Naruto would likely be very confused and hurt. He has always craved family love and acceptance, so this sudden turn would be a huge blow. He might try to plead with his family, asking them to believe him and give him a chance to explain.
In some fanfics, it could be related to a prophecy. His family might believe that Naruto is going to bring about a great disaster according to a misinterpreted prophecy. So, they turn on him in an attempt to prevent the prophecy from coming true, even though they are wrong in their understanding.
If Orochimaru were to turn Naruto into a girl in a fanfic, Naruto's personality could change in several ways. His boldness might be tempered a bit as he adjusts to his new form. He might become more cautious in some situations because he's now in a more vulnerable - looking body. However, his core values of loyalty and friendship would remain the same. He might also develop a new sense of femininity, which could add a new aspect to his personality. For example, he could be more nurturing towards his friends, something that was perhaps less emphasized when he was male.
One possible reason could be that they are too focused on their own problems or duties. Maybe they are involved in some important shinobi business that takes up all their time and attention, causing them to overlook Naruto.
They could start by showing him genuine love and acceptance. For example, his father could share all the things he sacrificed for Naruto in the past. His mother could cook his favorite meals, just like she used to dream about when he was a baby. And his friends in the family could show him how much they missed him and how empty the family feels without him.
His father, Minato, could be a likely candidate in a really dark fanfiction. Maybe he was resurrected in an imperfect way and his mind was warped, causing him to turn on Naruto.
If Kurama turns Naruto into a wolf, his relationship with the villagers would be a rollercoaster. Some villagers who were already distrustful of Naruto might see this as a sign that he is a monster. However, those who have come to know and love Naruto would be more accepting. They would see it as just another challenge for Naruto to overcome. His relationship with the other ninja animals in the village, like Akamaru, could also change. Akamaru might be able to communicate with Naruto in a way that other humans can't, and they could form a special bond. This could lead to new adventures where Naruto, in wolf form, teams up with Akamaru and their friends to protect the village.
Naruto's relationship with his mentor, like Kakashi, would face a big challenge. Kakashi would have to figure out how to train Naruto in this new form. Maybe he'd have to develop new jutsu specifically for Naruto as a fox. Also, Naruto's friends from the village, like Shikamaru and Choji, might treat him more like a pet at first, which Naruto would not be happy about, and this could cause some comical but also tense situations in their relationships.
He might try to prove himself. Naruto could focus on becoming stronger and more successful as a ninja. By showing his family that he can achieve great things and that he's a good person, he hopes to change their minds. For example, he might take on difficult missions and complete them with excellence.
If Naruto turns into a Digimon in a fanfic, it could also be due to a curse or a dark magic. He might start off confused and disoriented in his new form. However, being Naruto, he would quickly adapt. He could form an unlikely alliance with some Digimon characters. His Digimon form might have some sort of unique ninja - like attacks that are a combination of his original jutsu and the digital powers. For example, his Shadow Clone Jutsu could be transformed into a digital clone attack where the clones are made of digital energy.