The xkcd cartoon conflates the particular and narrow protections of the 1st Amendment of the U.S. Constitution with the older, broader, more general (and, if we’re honest, somewhat nebulous) principle of freedom of speech.
It is a great mistake to imagine that these things are the same. Doing so ignores the existence of non-governmental forms of censorship, including corporate censorship (e.g. internet filtering), and popular censorship via the tyranny of the majority -- or, for that matter, the tyranny of powerful minorities!
In an open society, you personally are supposed to recognize the freedom of others to speak. Via Why I think xkcd is wrong about Free Speech – Pat Kerr – Medium