In fanfiction, Naruto having the Rinnegan and being neglected by parents can lead to some really interesting character development. It could make him more self - reliant and distrustful at first. He might have to learn to harness the power of the Rinnegan on his own, without any parental guidance. This could result in him making some mistakes along the way but also growing stronger in unique ways.
One possible scenario in such a fanfiction could be that Naruto's parents are preoccupied with their shinobi duties. They might be constantly on missions for the Hidden Leaf Village, leaving Naruto at home with caretakers who don't really pay him much attention. This could lead to Naruto feeling lonely and isolated, just as he did in the original story when he thought he had no family.
One possible reason could be that they are too involved in their own shinobi duties. The world of ninjas is full of dangerous missions, and they might be constantly away on important tasks, leaving Naruto feeling neglected.
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.
A possible plot is that Naruto is constantly bullied because of his neglected state and his unknown bloodline. As he grows, he starts to show signs of his bloodline powers, which attracts the attention of both friends and foes. His journey then becomes about controlling his powers and dealing with the past neglect of his parents while also facing the new challenges that come with his revealed bloodline.
Naruto might try to seek attention elsewhere. He could focus on his training more intently. By pouring his energy into becoming stronger, he distracts himself from the pain of parental neglect. Also, his friends could play a crucial role. Their friendship might give him the sense of family and belonging that he lacks at home.
It has a huge impact. Naruto being neglected by his parents in crossover fanfiction can change the entire plot direction. Instead of having the usual drive to gain recognition from the village, he might be more focused on finding out about his parents and why they neglected him. This could lead him into different adventures and interactions. Maybe he'd be more likely to leave the village earlier in search of answers.
Well, in the fanfiction, Naruto might have some special abilities that are not recognized by his parents. In the Fairy Tail setting, this could translate to him having unique magic that he has to develop on his own because of the parental neglect. For example, he could discover a new type of elemental magic that no one else has seen before, all while struggling with the emotional pain of being ignored by his family. He may then use this newfound magic to gain the respect and friendship he craves within the Fairy Tail guild.
A plotline might involve Naruto starting to act out in negative ways to get his parents' attention. He could start getting into trouble at school or in the village. Maybe he would start to explore his own powers in secret, away from his family, and discover some unique abilities that he then uses to show his parents what they've been missing. Also, there could be a plotline where Naruto tries to build a relationship with his sister in secret, hoping that through her, he can get closer to his parents.
One common plot point is Naruto's search for his identity. Since he's neglected by his parents, he has to figure out who he is on his own. And with the Mokuton aspect, it often involves uncovering a hidden family connection related to Mokuton. Another is his struggle to gain power. He's determined to become strong using Mokuton to prove that he can succeed without his parents' support.