It's complicated because the most serious threat to free speech in the US right now is cancel culture, but most aspects of cancel culture are explicitly protected under the first amendment: "...or abridging the freedom of speech [private corporations choosing what to host on their websites, calling someone's employer and requesting that they be fired for what they said], or of the press [this garbage https://parade.com/news/simu-liu-under-fire-joke-batgirl-can... or the right of the people peaceably to assemble [twitter mobs, unless you count their speech as violence in which case we are back to square one], and to petition the Government for a redress of grievances [here, demanding that a government employee be fired https://www.change.org/p/ucla-fire-ucla-professor-gordon-kle...].