It could be that the fanfiction is causing some sort of disruption in the community or among the fans. Perhaps it contains false information about the sheriff's family that is spreading and causing problems. For instance, if it wrongly depicts family relationships, and the sheriff has to deal with the fallout from fans believing these false portrayals.
They're popular because it's an interesting dynamic. Stiles is a young, clever character and the Sheriff is an authority figure. Their relationship in the show has so many layers, and fanfiction allows fans to explore those layers further, like how they might support each other in different situations.
Perhaps the fanfiction alters the relationship between Kakashi and Naruto in a way that Kakashi doesn't like. Maybe it shows Kakashi as being overly harsh or unfair to Naruto in a situation where in the original series he wouldn't be. It could also be that the fanfiction contains plot elements that Kakashi, as a character, would find illogical or against the spirit of the Naruto world.
One common theme is family. Since Stiles is like a son to the Sheriff, many fanfictions explore this father - son like bond and how it evolves over time. For example, in some stories, they have to face challenges together that strengthen their family - like connection.
One possible reason could be a fundamental disagreement in their goals. Maybe Scott has a new mission that he believes Stiles would be a hindrance to, or perhaps their values have diverged. For example, if Scott becomes more involved with a new group that has a different ideology, he might feel the need to leave Stiles behind to pursue that new path.
One possible reason could be jealousy. Maybe Jackson has something Stiles wants, like popularity or a girl he likes. For example, if they both like Lydia, Stiles might get angry at Jackson's smooth ways with her.
There's a fanfiction called 'A Father's Love'. In this story, Sheriff Stilinski has to go to great lengths to protect Stiles from a powerful supernatural enemy. It shows their unwavering love for each other. Then there's 'Stiles and the Sheriff's Quest'. They embark on a journey together to solve a mystery that has haunted Beacon Hills for years, and their bond grows stronger throughout the adventure. Also, 'The Sheriff's Discovery' where the Sheriff finds out about Stiles' unique abilities and how to help him control them.
Maybe he finds Stiles' character in the original work very interesting and complex, and the fanfiction allows him to explore more about Stiles in different scenarios.
Maybe Stiles has been constantly disappointed by Derek's actions or lack of response in the fanfiction. It could be that Derek has repeatedly let Stiles down, and over time, Stiles just can't take it anymore.
Well, I really liked 'The Silent Protector' in the Stiles x Sheriff Stilinski fanfiction world. In this story, Stiles is in a really tough situation and the Sheriff is there to be his rock. It shows a side of their relationship that we don't always get to see in the show. 'Heart - to - Heart' is also good. It has a lot of emotional moments between them, like when they finally have an open conversation about all the secrets in their lives. And don't forget 'Guardian's Promise' which is about the Sheriff making a promise to always protect Stiles no matter what.
One possible reason could be that he feels he's a liability to the pack. Maybe he doesn't have the same supernatural abilities as the others and fears he'll hold them back during dangerous situations.