No, there is no First Amendment hate speech exception. Hate speech has no definition in case law, but it is generally understood to mean hurtful and offensive speech targeted against certain groups and individuals.
Very recently the United States Supreme Court held that the Patent and Trademark Office could not deny trademark registrations on the grounds that they were offensive, including that the proposed trademark contained racial slurs. “We have said time and again that the public expression of ideas may not be prohibited merely because the ideas are themselves offensive to some of their hearers . . . Speech that demeans on the basis of race, ethnicity, gender, religion, age, disability, or any other similar ground is hateful; but the proudest boast of our free speech jurisprudence is that we protect the freedom to express the thought that we hate.”
At CU Anschutz, we will make efforts to promote a culture of respect and civility, but we also recognize the constitutional boundaries that protect offensive speech.