Freedom of Speech (wiki) is granted by the First Amendment to the US Constitution (wiki) and protects many forms of speech, including those that are offensive, hateful, or just plain stupid. However, exception is made to speech that incites danger.
Disturbing the Peace (wiki) is a crime (misdemeanor) that seems to have more to do with loud noises and fighting (including challenging others to fights) than it does to the content of what is said. In fact, Disorderly Conduct (also a crime and related to disturbing the peace, wiki), includes "disturbing a lawful assembly of persons," but is, itself, subservient to the First Amendment. In other words, in considering charges of disturbing the peace, it seems that freedom of speech is given more weight than freedom of peace (not explicitly guaranteed, that I know of).
This all boils down to what appears to be, at present, a case-by-case basis, examined after the fact. Hence the Supreme Court hearing. Mid-next-year, after the Supreme Court decides on the case, we may have more guidance on the application of these seemingly at-odds provisions.
