A hate crime was a crime motivated by prejudice. Nazi Erich Zimmerman was, in the laws of the Teselecta, guilty of category three hate crimes. Because of this, they "left him to the antibodies". (TV: Let's Kill Hitler)
On the Sunlight Worlds, it was ruled by the Dalek Foundation that claiming the Daleks were evil was an example of a hate crime. The Eleventh Doctor was put on trial for committing the offence, first on Carthedia and later on Sunlight 349, both times with the Dalek Litigator acting as the prosecution. The Doctor pleaded guilty to the crime in attempts to anger the Litigator and get the Dalek to publicly display its true nature but the Litigator did not rise to the bait and the Doctor was exiled from the Sunlight Worlds. (PROSE: The Dalek Generation)