Naruto might be extremely heartbroken. He has always looked up to his mother, and being disowned by her would be a huge blow. He could become withdrawn and start to question his own worth.
It could also be due to some external influence. Perhaps an enemy used some kind of mind - control or manipulation on Kushina. They made her think that Naruto was a threat, so she decided to disown him. In the Naruto universe, there are many powerful villains who could potentially do this kind of thing.
It could also be due to a rift in their relationship over Boruto's ninja path. If Boruto decides to take a very different and unorthodox approach to being a ninja that Naruto doesn't approve of, such as using forbidden jutsu without proper understanding, Naruto might disown him in the fanfiction.
Another aspect could be that the fanfiction delves into how Kushina's presence affects Naruto's relationships with others. For instance, his relationship with Sasuke could be different. With a strong maternal figure in his life, Naruto might be more stable emotionally and be able to approach Sasuke in a more understanding way, which could potentially change the whole dynamic of their rivalry and friendship.
The disowning could also have an impact on the other characters. For instance, Hinata might be caught in the middle, trying to reconcile Naruto and Boruto. The other villagers might have different opinions about the situation. Some might side with Naruto, believing he had a good reason, while others might think Naruto is being too harsh on Boruto. This can add layers of complexity to the fanfiction's plot.
It could be due to a perceived betrayal. Suppose Naruto discovers some dark secrets within his family that he can't overlook. In his 'godlike' state, he might be more morally rigid and thus decides to disown them. For instance, if he finds out that his family was involved in some unethical ninja practices in the past, he would feel compelled to distance himself.
In some fanfictions, the authors might take creative liberties and create alternate universes where Naruto and Kushina interact in different scenarios. For example, they could be on a joint mission together, and through that, we see their personalities shine. Kushina's fiery nature and Naruto's determination would make for an interesting dynamic.
One possible fanfiction could be about Kushina finding Naruto in a situation where he's lost in a forest. Maybe she uses her unique chakra sensing abilities to track him down. It could be a heartwarming story of a mother reuniting with her son.
In certain fanfic concepts, Naruto could have found a special relic or artifact. This relic might have the power to reverse death. Since Naruto is always on adventures and exploring different places, he might stumble upon such an item and use it to revive Kushina. It could also be related to the Uzumaki clan's secrets that he uncovers which enables him to bring his mother back.
Minato could be a common character. Since he was Kushina's husband in the original story, his presence might add some interesting dynamics to the harem scenario. Another could be Jiraiya. His connection to Naruto and his reputation as a bit of a ladies' man could make for an interesting addition to the story.