Yes, there probably is. In the Naruto fandom, there are various fanfiction themes, and the 'narusaku' (Naruto - Sakura relationship) with Naruto hating Sakura can be an exploration of an alternative take on their relationship. Some fans might write this to explore what - if scenarios or to express their own views on the characters' dynamics that deviate from the canon.
One common element could be a significant event that causes Naruto to change his feelings towards Sakura. For example, he might discover something she did in the past that he can't forgive. Another element might be the exploration of how Sakura reacts to Naruto's hatred, which could lead to her character growth or downfall.
Well, in some Narusaku fanfictions, Sakura might hurt Naruto emotionally by choosing Sasuke over him repeatedly. This can make Naruto feel rejected and unloved, causing him pain.
In some narusaku fanfiction, Naruto might avoid Sakura because the story could be exploring different relationship dynamics. Maybe the author wants to create a more complex plot where Naruto has his own reasons, like he's focused on his ninja goals and doesn't want any distractions from Sakura at that moment.
In fanfiction, the evidence often lies in the way the author portrays Naruto's interactions. For example, Naruto may be shown being cold or dismissive towards Sakura, like avoiding her company or not showing any romantic interest. Meanwhile, with Hinata, he could be depicted as being more affectionate, like blushing around her or always coming to her aid. But it's important to note that this is all in the realm of fan - created interpretations and not the official canon.
One possible reason could be for the sake of creating a more complex love triangle in fanfiction. Maybe the writer wants to explore a different dynamic where Naruto and Hinata's relationship is strengthened by having a common dislike for Sakura. It could also be that the fanfiction writer is trying to give Hinata more agency and make her a stronger character by having her oppose Sakura in some way, perhaps in matters related to Naruto's affections.
Sometimes, in fanfiction, Sakura might use her medical skills against Naruto in a negative way. For example, if she withholds treatment or gives him a wrong diagnosis out of some conflicted feelings towards him. This is quite cruel and can cause both physical and emotional harm to Naruto.
It's appealing because it plays on the strong bond between Naruto and Sakura. Fans love to see Naruto in the role of a hero, especially when it comes to saving Sakura. It also adds more depth to their relationship.
There's also 'Naruto's Swift Rescue'. Here, Naruto senses Sakura is in danger through their deep emotional connection. He races against time, using his ninja skills to overcome various obstacles and finally saves Sakura from a group of rogue ninjas who had kidnapped her.
One reason could be that Naruto is afraid of getting hurt. If he has feelings for Sakura but isn't sure of her feelings towards him, he might choose to avoid her to protect himself. It's a common theme in many stories.