In an interview after the release of Goblet of Fire, J.K. Rowling stated,
[B]igotry is probably the thing I detest most. All forms of intolerance, the whole idea of "that which is different from me is necessarily evil." I really like to explore the idea that difference is equal and good. But there's another idea that I like to explore, too. Oppressed groups are not, generally speaking, people who stand firmly together – no, sadly, they kind of subdivide among themselves and fight like hell. (source)
Even though wizards already have enough trouble trying to keep themselves secret from Muggles, the Death Eaters have to make everything harder by creating a hierarchy within the wizarding world between "purebloods," "Mudbloods," and "blood Traitors." And then non-Death Eaters have to go and give in to hatred of other groups too: Hagrid is a target because he's half-giant. Ron is a target because he's poor. Harry is a target because he is powerful and different. As Hagrid puts it, "everythin' seems ter happen ter you [Harry], doesn' it?" (18.54). His fame makes Harry an object of hatred for some wizards, including Draco Malfoy.