My understanding is that immediate incitement to violence - something like, "Hey, that guy there is a commie! Get him!" - can be made illegal and is in some places.
General advocacy - like, "Commies should be lynched!" - is protected speech.
Unless someone more lawyerly than me beats me to it, I might try to find some cites when I have time.
I think that actually summarizes things relatively well.
From my understanding, making slurs, insults, racist statements, etc. is still protected speech as it pertains to the First Amendment. As you indicated, making a direct
threat against an individual or group is what essentially crosses the line. But ultimately, just a standard verbal statement regarding someone or some group does not in an of itself constitute a crime.
In other countries, it is different. Canada for example (where I grew up) actually has laws in place regarding what types of speech might land you in trouble from a legal standpoint. Don't recall all the details, but certain statements against specific ethnic groups and minorities can result in in certain legal ramifications. To note, in most cases I am aware of, the result is usually a fine. There is a wikipedia page that outlines some of the hate speech laws in Canada:
Hate speech laws in Canada - Wikipedia