The Supreme Court has listed various restrictions on free speech (below), such as yelling "Fire" in a crowded theater. I'm not sure I see much distinction between that and lying to incite hatred and violence against people.
For example: there are public figures who claim trans people molest young children in public bathrooms. This claim is simply not true - trans individuals are the victims of sexual crimes at a higher-than-normal rate, not the perpetrators. Knowing this, I can understand an argument that people spouting this hateful and inciting lie shouldn't be given a platform. I can certainly understand protesting strongly against allowing such an individual to speak at my school or in my community.
The Supreme Court has held that "advocacy of the use of force" is unprotected when it is "directed to inciting or producing imminent lawless action" and is "likely to incite or produce such action". In Brandenburg v. Ohio (1969), the Supreme Court unanimously reversed the conviction of a Ku Klux Klangroup for "advocating ... violence ... as a means of accomplishing political reform" because their statements at a rally did not express an immediate, or imminent intent to do violence. This rule amended a previous decision of the Court, in Schenck v. United States (1919), which simply decided that a "clear and present danger" could justify a congressional rule limiting speech. The primary distinction is that the latter test does not criminalize "mere advocacy".
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'".
Threats of violence that are directed at a person or group of persons that has 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. However, sometimes even political speech can be a threat, and thus becomes unprotected.