Even when the perpetrator mistakes a victim as having a characteristic towards which the perpetrator has a bias, such an offense is still a hate crime.
When identifying whether an offense can be considered to be a hate crime, it is actually more important to identify whether the perpetrator’s actions were undertaken because the perpetrator wished to express hatred towards people with a certain characteristic, rather than finding out whether the victims actually possessed such a characteristic.
Even in cases where the victim does not possess the characteristics towards which the perpetrator has a bias, the offence is considered a hate crime. This is because a hate crime will be considered as such if the criminal offence was committed against the victim because of the victim’s actual or supposed characteristics (sex, nationality, religion, ethnicity, sexual orientation etc.)
example A man was attacked on the street by a perpetrator because he was Moroccan. The perpetrator was motivated by the idea that the man was a Muslim, although he was an atheist. In this case, the perpetrator of the violence can be convicted of a "hate crime" for expressing hatred towards Muslims, even if the victim does not actually belong to that religion. The fact that he made a mistake in perception does not diminish his guilt.
It should be kept in mind that such crimes are not generally aimed at specific victims on a personal basis, but rather the whole community possessing a common characteristic. Hate crimes are committed as a way of sending a message to not only the victim, but also to the larger community to which that victim belongs. Thus, even when the perpetrator mistakenly chooses a victim who does not possess the characteristic in question, the offense is more serious than an offense without a biased motive, and it is still considered to be a hate crime because the perpetrator’s motive was based on hatred.