In some fanfictions, the Cullens might hate Bella because of jealousy. Maybe other vampires are jealous of the attention she gets from Edward. Another reason could be that she brings too much danger to their family. Her presence could attract unwanted attention from other vampires or vampire hunters, which puts the Cullens at risk.
Well, it could be due to the way the Cullens interact with the other people in Forks. If Bella notices that they are being manipulative or using their powers in a way that she doesn't like to influence the townspeople, that could make her start to hate them. Also, if there is some kind of power struggle within the Cullen family that starts to affect Bella negatively, like she gets caught in the middle of it or she sees how it's causing harm to those she cares about, she might turn against them.
It's possible that in the fanfiction, the Cullens are involved in some sort of betrayal. For example, they might side with someone who is against Bella. This act of betrayal would be a strong reason for her to hate them. In fanfiction, new storylines can be created where the Cullens' actions are not in line with what Bella expects or desires, which can result in her hatred.
In some fanfictions, Bella might accidentally harm one of the Cullens, either physically or emotionally. This could lead to them hating her. Also, if she were to side with their enemies in a conflict, that would definitely make them dislike her. For example, if there was a feud between two vampire groups and Bella chose the wrong side, the Cullens would not be happy with her.
In the original Twilight story, Bella is initially attracted to the Cullens, especially Edward. But in this fanfiction where she starts to hate them, it's a complete contrast. It shows a different side of Bella's character, one that is more critical and less forgiving. In the original, she is more likely to overlook their flaws because of her love for Edward. Here, she focuses on the negative aspects.
She might start by giving them the silent treatment. Just ignoring them completely when they try to talk to her, which would be a very human way of showing anger.
It could be another vampire clan. Maybe they are jealous of the Cullens' interest in Bella or they think that Bella's presence among the Cullens will disrupt the balance of power among vampires. So they try to get Bella from the Cullens, making them the main antagonists.
It could be that the fanfiction writer took a different approach to the story. In some fanfictions, the Cullens could be involved in situations that go against what Bella stands for. Perhaps they are written to be more secretive and untrustworthy, leading to Bella's hatred.
I'm not sure specifically as there could be many different takes on it. Generally, it might be about Bella using her singing in a context related to the Cullen family in a fan - created story.
Yes, it is quite common. Fanfiction writers often use this scenario to explore the relationship between Bella and the Cullens. It gives an opportunity to show the Cullens' caring side towards Bella.