The Akatsuki could also feel a sense of sadness or betrayal in this 'neglected' scenario. For example, some members might have had a certain respect or even a strange kind of hope for Naruto. So, when they are neglected, it shatters that idea they had. They might then become more withdrawn and brood over this new situation, which could lead to changes in their group dynamics and individual characters.
Perhaps the Akatsuki's neglect is a part of a much larger plan by Naruto himself. He might be trying to lull the Akatsuki into a false sense of security while he's actually gathering information or power in the background. Then, when the Akatsuki least expects it, Naruto reveals his true intentions and uses the situation to his advantage, which would be a huge plot twist for the readers who thought Naruto was just being mean or indifferent.
In this kind of fanfiction, Naruto might be neglected by his village. He could be feeling alone and unappreciated. So, he decides to join the Akatsuki. Maybe he sees them as a group that could accept him for who he is, regardless of his past in Konoha. He might start to learn their ways and use his skills for their missions.
It could be the Hidden Leaf Village itself. Since Naruto was neglected there, the village's leadership or some of the villagers who shunned him could be seen as antagonists. They pushed Naruto towards the Akatsuki by not giving him the support he needed.
Their relationship could start with mistrust. Naruto, having been taught that the Akatsuki are bad, would be wary of the female member. But as she shows him kindness in the face of his neglect, he might start to warm up to her. For example, she could bring him food when no one else in the village does.
Another storyline could involve the female Akatsuki member using Naruto's situation of being neglected to her advantage. She could try to convince him to join the Akatsuki, promising him a place where he would be valued. However, Naruto would have to struggle with the moral implications of joining a group that is considered evil. As the story progresses, he might end up changing the Akatsuki from within instead.
Well, in this fanfiction, it could be that Akatsuki has a change of heart. Some members might realize that Naruto represents a hope for the ninja world in a different way than they initially thought. So they step in to save him when he's in a really tough situation, like being trapped in a powerful jutsu or surrounded by a large number of enemy ninjas. They use their own unique skills, like Kisame's water jutsu or Itachi's Sharingan abilities to fight off the threats.
Perhaps he's been influenced by someone who gives him bad advice. For example, if someone tells him that natural talent is enough and training is overrated. Also, he could be dealing with some personal problems, like a conflict within his family or among his friends that takes up all his time and mental energy, causing him to neglect training.
He might start to rely on his friends more. For example, Sasuke and Sakura could become his main source of emotional support. He would focus on training with them and sharing his feelings, which in turn helps him to grow stronger and more independent.
Pain would be one of the most challenging. His Rinnegan gives him a wide range of powerful abilities like the Six Paths of Pain. Naruto would have to figure out how to counter each of those paths and find a way to reach the real Pain. Itachi is also tough. His Sharingan and genjutsu skills are top - notch. Naruto would need to break free from his genjutsu and then find a way to fight back against his fire - based attacks.