Yes. Hate speech is usually defined as speech that offends or attacks people on the basis of race, ethnicity, national origin, religion, gender, sexual orientation, disability, disease, or other traits. It is protected by the First Amendment. Hate speech can only be censored or punished by the government if it falls into one of the unprotected categories of speech--for example, if it contains a true threat to cause bodily harm to someone else, or was used to incite immediate lawless action.
Why does the First Amendment protect such repugnant speech? Because allowing the government to censor hate speech would amount to giving the government the power to define what is and is not offensive. This could eventually lead to the erosion of everyone's free speech rights. After all, the same laws that can be used to silence bigots can also be sued to silence you. To paraphrase Justice Louis Brandeis, the remedy for speech we don't like isn't enforced silence--it's more speech.