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.
One possible plot twist could be that her family has a secret reason for neglecting her. Maybe they're trying to protect her from some greater danger. Another could be that she discovers she has a hidden power that makes her family regret their neglect.
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.
One plot twist could be that Naruto discovers his parents had a very good reason for their neglect, like they were protecting him from a greater danger. Another could be that the village elders knew about the neglect but did nothing, and Naruto has to confront them. Or perhaps Naruto finds out he has a secret power that was the cause of his parents' seeming neglect, as they were afraid of what he could do.
One possible plot twist could be that the Akatsuki initially saves Naruto for their own self - serving reasons. For example, they might want to use him as a bargaining chip against Konoha. But as time goes on, some members of the Akatsuki start to develop a real sense of comradeship with Naruto. They see his determination and the good in him, and this changes their perspective on the whole shinobi world.
A plot twist might be that Naruto discovers that the Akatsuki was actually formed with good intentions in the past, but got corrupted over time. As the leader, he decides to go back to the original purpose. He then has to fight against the current power - hungry members while also trying to convince the other villages that the Akatsuki can be a force for good again. This would create a lot of tension and interesting character dynamics.
One possible plot twist could be that Naruto joins the Akatsuki to spy on them for Konoha. But as he spends more time with the members, he starts to understand their motives, which are not all as evil as he initially thought. For example, some might be seeking revenge for past wrongs done to their villages.
Well, perhaps in the fanfiction, Naruto kills Orochimaru and the Akatsuki, but it turns out that Orochimaru had a failsafe. His death triggers a powerful curse that starts to affect Naruto and the Hidden Leaf Village. Naruto then has to find a way to break this curse while also dealing with the remaining threats that were associated with the Akatsuki. It could be a race against time to save the village and himself.
Well, they might join Akatsuki in fanfiction because they think they can change the organization from the inside. Naruto, with his strong belief in redemption, could believe that he can turn the Akatsuki members to the good side. Sakura, who always stands by Naruto, would follow him. Once inside, they would face a lot of challenges. The Akatsuki members are all very powerful and have their own motives. Naruto and Sakura would have to deal with the likes of Itachi and Kisame. Itachi might see through their plan, or they might actually start to understand Itachi's own complex situation and motives which could lead to a whole new set of developments in the story.
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.
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.