They could view him as a potential recruit. If Harry has been abused, they might think he could be turned against those who he was supposed to be with, like the good wizards. They would see his abuse as a way to break his loyalty to the side of good and bring him into their dark ranks. For example, they might offer him power and protection from his abusers in exchange for his allegiance.
On the other hand, some of the more cruel Death Eaters might see his abuse as a sign of weakness. They could then target him even more, thinking that he is an easy prey. In their view, an abused Harry is a broken Harry, and they might want to finish him off, either out of sadism or because they fear he could still become a threat if he overcomes his abuse.
In some fanfictions, the Death Eaters might see Harry as a tool. If they find out he's abused, they could try to manipulate him. They might think that with his power and now his vulnerability, they can turn him to their side, using his anger at his abusers as a driving force.
His magical education would be very different. Instead of learning at Hogwarts, he might be taught in some dark and secret location by Death Eater instructors. They would likely focus on dark spells and hexes.
Their view could become more confused. Fanfiction can present all sorts of alternate universes and character developments. The Death Eaters, used to a very specific view of the wizarding world under Voldemort, would find it hard to accept different versions. They might see the wizarding world in fanfiction as a chaotic and wrong place, which would make them double down on their own views to feel more secure.
It would likely worsen their relationship at first. Aunt Marge is very set in her ways and has a narrow view of the world. Discovering Harry is a wizard would be a huge shock to her system, and she would probably be very unkind to Harry.
They might start to see Harry as a victim rather than just an enemy. Their view of him could become more sympathetic.
Snape might start to see Harry as a survivor. The scars could represent all the challenges Harry has faced, and Snape could respect that on some level.
Perhaps there is a prophecy that the Death Eaters misinterpret at first. They think killing Harry is the right thing, but later they discover that saving him is actually crucial for their own survival or for some greater good in the wizarding world. So they decide to go against Voldemort's orders and save Harry. For instance, they find out that Harry has some power that can prevent a much greater evil from emerging, which would also threaten the Death Eaters.
The Hogwarts students would be divided. Some would be in disbelief and would still hope that Harry has a good reason for joining. They might secretly support him. Others, especially those who have lost family members to the Death Eaters, would be furious and see Harry as a traitor. Harry's old enemies at Hogwarts, like Draco Malfoy, would also be confused. Draco might initially think that Harry has finally seen the 'right' side, but as he realizes Harry's true intentions (if they are good), he would be conflicted as well since he's been brought up in a Death Eater - influenced family.
Well, one possibility is that Harry would be forced to learn dark magic. The Death Eaters might try to mold him into one of their own, but Harry's strong sense of good might resist. He could secretly plot against them while pretending to go along with their ways.
It makes the Malfoy family seem more dysfunctional. Lucius is seen as a cruel abuser, which is a new and darker side to his character. And Draco becomes a more sympathetic figure, as we now understand that his upbringing was not as privileged as it seemed. It shatters the image of the powerful, united Malfoy family presented in the original series.