For all it's worth, I agree with Nite Mite and AGB. While it is by no means uncommon that hate crimes involve racist sentiments, not all implicate race. On the other hand, it seems to me that berndjot's suggestion recognized this distinction at least somewhat by suggesting the German translations of "rassistisches Verbrechen" AND "Verbrechen gegen Angehoerige einer Randgruppe."
However, I am quite sure that victims of hate crime do not necessarily have to be members of a "Randgruppe." In the other discussion, cited by Nite Mite, Mark suggested that "hate crime" might be translated as "politisch motivierte Kriminalitaet," at least as a general category. That same discussion also quoted the FBI as describing "hate crime" as crime being "motivated in whole or in part by a bias against the victim's perceived race, religion, ethnicity, sexual orientation, or disability" (and that's the definition I am familiar with). At least technically, then, the victim may not be a member of a marginal group, but actually could be a member of a majority.