Well, it could make Hermione a lot more conflicted. Growing up with Death Eater parents, she might constantly struggle between the values she's exposed to at home and the ones she discovers at Hogwarts. For example, she might initially be more hesitant about befriending Harry and Ron due to her family's possible prejudice against 'blood traitors'. This could lead to a more complex and nuanced character arc as she gradually breaks away from her family's ideology.
Well, in some fanfictions, Hermione might use her superior intellect. She could outwit the Death Eaters by setting up elaborate magical traps. For example, she could use transfiguration magic to create objects that suddenly turn into something dangerous when the Death Eaters approach. Another way could be through her extensive knowledge of potions. She might create a potion that incapacitates or kills them when they come into contact with it.
In some fanfictions, Hermione's adoption might make her more self - reflective. She may question her identity more often, leading to a deeper understanding of herself. For example, if she discovers she was adopted from a different magical culture, she might explore that culture and in turn, become more open - minded.
This abandonment could make Hermione more independent. She might have to learn to fend for herself earlier, relying less on others for emotional support. It could also make her more distrustful at first, but as she grows, she might learn to open up again through the friendships she forms, like with Harry and Ron.
If Hermione joined the Death Eaters in fanfiction, it would completely turn the original plot on its head. The Death Eaters are known for their dark magic and prejudice, which is the opposite of Hermione's values. This could lead to a very different kind of story, perhaps one where she tries to change the Death Eaters from the inside, or she could be a double agent. It would be a very dark and complex alternate universe.
She loses her moral compass. Normally, Hermione is a very ethical character, but in these fanfictions, she may start to see the dark arts as a viable option without hesitation. This could lead to her making choices that harm others, like casting harmful spells on those who oppose her.
She becomes more in tune with nature. As a centaur, Hermione is closer to the natural world, and this makes her more aware of the environment around her. For example, she starts to notice small changes in the forest that she might have overlooked as a human - shaped witch.
If Hermione was adopted by the Cullens, her character would likely become more attuned to the vampire world's values. She might be more secretive like the Cullens, as they hide their true nature. Her studious nature could be redirected towards understanding vampire lore. For example, instead of poring over Hogwarts textbooks, she'd be delving into books about vampire history and abilities. This new family dynamic would also make her more cautious in her interactions, knowing the potential danger her new family could face if exposed.
Well, her character would likely become more guarded. Snape is not one for open displays of affection or warmth, so Hermione might learn to hide her emotions more. However, she would also be exposed to Snape's vast knowledge of potions and the Dark Arts in a more intimate way. This could make her more of an enigma to her friends. She might start to question some of the Gryffindor values she once held dear, as Snape would surely instill in her a different set of beliefs, at least to some extent.
On the other hand, she could also become more empathetic. If she is trying to redeem the Death Eater, she has to understand his motives and background. This could lead to a deeper understanding of the people who are drawn to the Dark side, and she may become more forgiving in general. For example, she might start to see that not all Death Eaters are irredeemable monsters.
Hermione might become more protective. If her twin is in any sort of danger or facing difficulties, she would step up more. For instance, if the twin gets bullied for being different, Hermione would use her wits and knowledge to stand up for them.