It could be a revenge plot gone too far. Suppose her parents did something in the past that she just found out about, and in her new dark persona, she decides to take the ultimate revenge. Or perhaps she has fallen so deep into the dark side that she no longer values family and sees them as just another obstacle in her path of darkness.
One possible motive could be jealousy. Hermione is highly intelligent and often outshines Draco in academics. In a twisted version of a rivalry, Draco's envy could turn into a deadly hatred. Another could be his family's influence. If the Malfoys push him to take extreme actions against Muggle - borns, Hermione would be a prime target.
One possible motive could be blackmail. Maybe the dark forces have something on her or her loved ones that forces her to spy for them. Another could be a thirst for knowledge. In the 'Harry Potter' series, Hermione is always eager for knowledge. If she thought the dark side had some unique knowledge or power she couldn't get elsewhere, she might be tempted to side with them, at least as a spy.
Another motive might be related to a dark object influencing her. If Hermione came across a cursed object, like a dark locket that amplified negative emotions such as envy or fear, it could drive her to kill Harry. Maybe she started to envy Harry's fame and the special attention he always got, and the locket pushed her over the edge.
If such a fanfiction exists, perhaps the motive could be a misdirected attempt at protecting the greater good. Maybe Dumbledore thought Hermione's parents were in some way a threat to the wizarding world's secrets that he was trying so hard to protect. But this is still a very far - fetched idea as Dumbledore was always about protecting life in the official story.
Differing ideologies during the wizarding war. If James was seen as a threat to Snape's side (even if Snape was on the wrong side, from a moral perspective), Snape could justify killing him. For example, if James was too aggressive in fighting the Death Eaters and Snape thought it would lead to more bloodshed, he might take matters into his own hands to stop James.
One possible motive could be revenge. The Dursleys treated Harry awfully for years, so in fanfiction, he might reach a breaking point. Another could be self - defense if the Dursleys in the fanfiction were to take their abuse to an extreme level.
A possible motive could be revenge. If a dragon had hurt someone he loved, like his father or Astrid, he might be driven to kill it. It would be a very emotional and difficult decision for him, but his love for his friends and family could push him to that extreme.
One possible motive could be jealousy. If Kiba were to gain more recognition in the village than Naruto in the fanfiction world, Naruto's insecurities could drive him to do something drastic like killing Kiba. But this is a huge departure from his usual self.
Well, in some fanfictions, it could be that they're under the influence of some dark magic or a spell that makes them turn against Hermione. Or perhaps they're misinformed about her actions at Hogwarts and think she's a bad influence. Also, some writers might use it as a plot device to create a rift and then build a story around Hermione trying to fix things with her parents.
One possible reason could be her involvement in the wizarding world. If her parents are muggles and they find out about the extreme dangers she faces in the magical realm, they might disown her out of fear for her safety. Another reason could be if she starts to show more loyalty to the wizarding community than to her muggle family, making them feel like she no longer belongs with them.