He would probably be very lonely. Without a family, Naruto has no one to turn to in the most basic sense, which would lead to a deep - seated loneliness.
In this fanfiction, Naruto would likely experience a complex mix of emotions. He could start with confusion, not understanding why his family left him. This confusion might turn into self - doubt, wondering if there was something wrong with him. As he grows older, the sense of abandonment could lead to resentment. Resentment towards his family and towards the village that didn't seem to do anything to prevent it. However, he might also have a glimmer of hope. Hope that he can create his own family or find people who truly care about him in a way that his biological family didn't. This emotional rollercoaster would shape his character in a very different way from the Naruto in the original series.
There would be a lot of anger. Naruto might be angry at his parents for leaving him, and this anger could fuel his determination in some ways. For example, he could strive to become a great ninja just to prove that he didn't need them. But it could also cause problems in his relationships, as he might lash out when reminded of his abandonment.
Naruto would be confused. He's grown up believing that the village is his home and the villagers are his family, at least in a sense. So when they start torturing him, he can't understand why. This confusion would mix with his pain and anger. He might also feel a sense of loneliness that is deeper than anything he's ever felt before. Even though he has friends like Iruka - sensei, the fact that the villagers as a whole are against him would make him feel isolated. However, his inner hope and the belief that things can change would keep him from completely breaking down.
Naruto in such a fanfiction could have a very different growth trajectory. Abandoned by family, he might be more eager to find a sense of belonging elsewhere. He could be more drawn to groups or individuals who seem to accept him unconditionally. His view of the village might also be more cynical. He may see the village as a place that failed him by allowing his family to abandon him. His training could be more solitary as he doesn't have a family to guide or encourage him. This would likely lead to a Naruto with a more independent and perhaps more hardened personality compared to the Naruto in the original story.
Kushina would most likely experience deep remorse. Remorse for not being there for Naruto when he needed a mother. There could also be a sense of longing in her, longing to be part of Naruto's life and to make up for all the lost time. And of course, she might be filled with self - loathing for her past actions.
A plot twist might be that Naruto, after being abandoned by his family, finds a new 'family' in unexpected places. For example, he could bond closely with a group of outcasts in the village who understand his pain. Or perhaps, the family's abandonment was part of a larger conspiracy within the ninja world, and Naruto's journey to uncover the truth behind it becomes a major part of the story.
Perhaps Naruto starts to question his own identity. Since he was abandoned by his family, he could be on a journey to discover his true heritage and in the process, his dark side grows as he faces many hardships and betrayals. He may then use his new understanding to either wreak havoc or find a way to forgive and move forward.
One possible plotline could be Naruto growing up on his own, learning survival skills at a very young age. He might become more cynical towards the idea of family. Another could be that he meets someone who becomes like a surrogate family, and through this relationship, he starts to heal his inner wounds. He could also start to search for the reasons why his family abandoned him, leading to a journey of self - discovery.
One possible plotline could be Naruto growing up on his own, learning survival skills in the streets of Konoha. He might become more distrustful of others at first. Another could be him seeking out his family's secrets on his own, leading to unexpected adventures. Maybe he'll find a new family in his friends, like Sasuke and Sakura, who support him in ways his biological family didn't.
He would likely feel a great sense of anger. Naruto has a strong will, and this betrayal would fuel his anger. He might be determined to find out the truth and get revenge on those who wronged him. At the same time, he would also be in deep pain. It's like losing the most important thing in his life. This emotional turmoil could lead to a change in his personality, making him more withdrawn and less optimistic than before.
One possible reason could be some sort of dark force influencing Kushina's mind. Maybe she was under a powerful genjutsu that made her think she had to abandon Naruto for his own safety, even though it was a false perception.