Should racist remarks be subject to criminal prosecution?

There seems to be some confusion on this subject.. This may help but it would appear ultimately it's still not clear cut.

In Chaplinsky v. New Hampshire (1942), the Supreme Court held that speech is unprotected if it constitutes "fighting words". Fighting words, as defined by the Court, is speech that "tend[s] to incite an immediate breach of the peace" by provoking a fight, so long as it is a "personally abusive [word] which, when addressed to the ordinary citizen, is, as a matter of common knowledge, inherently likely to provoke a violent reaction". Additionally, such speech must be "directed to the person of the hearer" and is "thus likely to be seen as a 'direct personal insult'".

“True threats of violence” that are directed at a person or group of persons that have the intent of placing the target at risk of bodily harm or death are generally unprotected. However, there are several exceptions. For example, the Supreme Court has held that "threats may not be punished if a reasonable person would understand them as obvious hyperbole", he writes. Additionally, threats of "social ostracism" and of "politically motivated boycotts" are constitutionally protected.