Thom Hartmann (RT commentator) once conducted a man-on-the-street survey in Seattle in which he demonstrated that while out of ten ordinary Americans who defend the First Amendment, seven would tolerate censorship of topics which opposed their most controversial beliefs and opinions. Those seven did not believe their support of censorship violated the First Amendment.
With specific reference to every conventional print or digital medium I can think of, from the New York Times to this forum, use of the word, n!gger, is brazenly and routinely censored. In spoken media, use of the aggravatingly stupid and cringingly accommodating phrase, "n-word," is used in place of n!igger, even when the word is used academically (as in this comment), not insultingly, or as innocently as when quoting Mark Twain. And I will wager a pension check those who instinctively comply with self-censoring refusal to use that word will insist they support the First Amendment.
"The American Negro will not be truly free until the word, "n!gger," no longer troubles him. Because the striking of chains and the death of Jim Crow does not free the mind." (James Baldwin, speaking at Columbia University, September, 1974.)