In a fanfiction with this scenario, it would create a huge rift. Hermione would probably question everything about their friendship. Harry's use of the term 'Mudblood' goes against the values they are supposed to uphold together. Their relationship would be in turmoil. It could lead to Hermione isolating herself from Harry and his friends. For the relationship to be mended, the fanfiction would need to show a strong arc of Harry realizing his mistake, learning about the harm of such slurs, and making it up to Hermione in a meaningful way, like protecting her from those who use such derogatory terms.
It could completely shatter their relationship at first. Hermione, being proud and intelligent, wouldn't tolerate such an insult easily. Their friendship might seem irreparable. However, if the story is about growth and redemption, Harry would have to go through a lot of self - reflection. He'd need to understand the depth of his wrong and work towards winning back Hermione's trust, perhaps by standing up against those with discriminatory views more actively in the story.
Yes, there might be some fanfictions out there that explore darker or more complex storylines where such a thing could happen. However, this goes against the positive growth of their relationship in the original 'Harry Potter' series. In the canon, Ron's use of that term was a regrettable moment of weakness, and most fanfictions tend to uphold the characters' better natures.
In some fanfictions, this incident could be a turning point for Hermione. She might decide to focus more on her studies and magic skills, distancing herself from Ginny and those who tolerate such slurs. This could then lead to her achieving great things on her own, away from the drama, and eventually making Ginny realize the mistake she made.
Some fanfictions might have Hermione immediately cut Ron out of her life. She's a strong - willed character, and such a hurtful comment could be the last straw. This would then lead to a story about her moving on without him and finding new friends or allies.
It deteriorates rapidly. Lily is likely to be extremely hurt and angry. She probably won't be able to forgive Snape easily, if at all. Their relationship which might have had some complexity and depth before, turns into one of animosity from Lily's side.
Well, it makes their relationship more of a paternal - son - like bond. Harry, being called daddy, would likely feel a sense of responsibility towards Draco. He might be more protective and nurturing, like a father would be.
Well, it changes a lot. For example, Harry would have more emotional support right from the start. Hermione, being his sister, would be more likely to be by his side constantly. So in the early years at Hogwarts, she might be able to prevent some of the bullying he faces from Snape or Draco.
Well, if Hermione is Harry's sister in fanfiction, their relationship becomes more of a family - based one. They would have a deeper, more instinctive bond. Harry might be more protective of Hermione, like an older brother would be. And Hermione could be more likely to give Harry sisterly advice, rather than just being a friend.
Well, if they are siblings in fanfiction, they would probably have a more protective relationship. Harry might be more over - protective of Hermione, like a big brother. And Hermione could be constantly looking out for Harry's well - being too. Their bond would be deeper and based on family loyalty from the start.
The relationship between them can be a journey. Initially, there could be some envy or misunderstanding due to the house differences. Maybe Harry envies the academic resources Hermione has in her house, or Hermione doesn't understand some of the Gryffindor bravado. But as they interact more, they learn to appreciate each other's strengths. Harry might admire Hermione's ability to think outside the box of Gryffindor norms, and Hermione could come to respect Harry's leadership skills that are so characteristic of Gryffindor. This new - found respect and admiration transform their relationship into a more profound and unique friendship.
If Hermione realizes her mistake and tries to make amends, it could lead to a deeper understanding between them. They might have to work through their feelings and have some difficult conversations. For instance, Hermione might have to explain her reasons fully, and Harry would have to decide if he can forgive her.