This is actually a more nuanced issue than it appears to be on surface level.

"Whites" are legally protected by hate crimes laws both within the laws themselves, and within the constitution's requirement they receive equal protection of the laws. Therefore, it's a moot point to determine if racism is a factor in the case of "black" on "white" crime for prosecution, since racism alone is not the only factor needed for prosecution. What is relevant to determine prosecution for a hate crime is whether any race or some other "protected characteristic" not "protected groups" was a factor in why a person targeted that/those individual/s to be their victim. e.g. If a "black" person targets a "white" person to be their victim simply because of his/her race or perceived race, whatever their accompanying rationale, they would be subject to hate crime prosecution. However, it's not without merit to determine their rationale, because it's within their rationale that one may verify if a true hate crime has been committed. This is why hate crimes are difficult to prosecute, because they essentially involve prosecuting thoughts rather than physical crimes, which are easier to prove.

https://en.wikipedia.org/wiki/Hate_crime_laws_in_the_United_States#Classification_of_crimes_committed_against_Caucasians

In this case however, yelling a racial slur prior to assault makes it pretty clearly a hate crime.