In the fanfiction, it could be that Sakura has had some past experiences that made her vulnerable. For example, she might have been seriously injured in a previous mission. Team 7, having witnessed that, now wants to be extra careful and overprotective of her. Also, Sakura may represent something pure or essential to the team's morale, and they don't want to see her in harm's way, so they go overboard with protecting her.
Maybe they have a deep emotional bond with her. Naruto and Sasuke might see her as a dear friend or even like family. So they feel the need to protect her just like they would protect their own family members.
One reason could be her importance to the team. Sakura might have some special skills or knowledge that they don't want to lose. So they protect her to ensure the team's overall strength.
One reason could be that they are comparing her to the more physically powerful members like Naruto and Sasuke. Naruto has the Nine - Tails' power and Sasuke has the Sharingan. In comparison, Sakura's initial abilities seem less flashy. Another reason might be that they haven't seen her full potential yet. Maybe she hasn't had a chance to show off her improved combat skills or her advanced medical ninjutsu in front of them.
One reason could be guilt. Since Minato wasn't there for Naruto when he was growing up in the original story, in the fanfiction, he might be overcompensating for that lost time. He feels like he has to make up for all those years he wasn't around to protect his son.
Well, in such fanfiction, it could be shown by team 7 members always coming to Sakura's rescue immediately. For example, if she's in a fight, they might jump in even before she has a chance to defend herself fully. They might also constantly worry about her well - being and not let her take on dangerous missions alone.
One possible reason could be a powerful enemy attack. Maybe she was caught in a fight against a much stronger foe who used a deadly jutsu on her. Another reason might be a self - sacrifice. Sakura could be in a situation where she has to give up her life to save her teammates from Team 7.
One possible reason could be that she sacrifices herself to save Naruto from a powerful enemy. In the heat of battle, she might put herself in harm's way to ensure Naruto's survival.
One possible reason could be Sasuke's continued obsession with his revenge - even after they got married, his focus on past grudges might have driven a wedge between them. Another could be differences in their life goals. Sakura might have wanted a more settled family life, while Sasuke was still drawn to his wandering ways in the name of protecting the village from afar.
One possible reason could be that the fanfiction misrepresents Sakura's character. Maybe it portrays her in a way that she would never act in the original context of the series, which makes her seem out of character and thus causes dislike. Another reason might be that the fanfiction focuses too much on other members of Team 7 and sidelines Sakura, making her seem less important or relevant than she actually is in the story.
It could be because of a dark curse. Suppose Naruto was cursed by an ancient evil. This curse slowly ate away at his sanity and made him view his friends in Team 7 as threats. As the curse took over more and more, he finally reached a point where he killed them. However, this would require a lot of backstory and character development in the fanfiction to make it somewhat believable.
One reason could be jealousy. If in the fanfic, Sakura gets closer to someone else Naruto cares about, like Sasuke in a different way than he expected, it might make him hate her. For example, if Sakura teams up with Sasuke against Naruto's wishes in the fan - created plot.
Protectiveness. Sasuke has seen a lot of danger in his life. He knows Sakura is a valuable person, both as a friend and as someone he cares about. So his possessiveness could stem from his desire to keep her out of harm's way. He doesn't want any bad guys to get near her.