[JoeRedskin]

The seminal case on free speech and its limitations is Chaplinsky v. New Hampshire, 315 U.S. 568 (1942):

There are certain well-defined and narrowly limited classes of speech, the prevention and punishment of which have never been thought to raise any constitutional problem. These include the lewd and obscene, the profane, the libelous, and the insulting or "fighting words" those that by their very utterance inflict injury or tend to incite an immediate breach of the peace. It has been well observed that such utterances are no essential part of any exposition of ideas, and are of such slight social value as a step to truth that any benefit that may be derived from them is clearly outweighed by the social interest in order and morality.

(emphasis mine)

Fighting words are not simply words that are "offensive". Further, you can't target specific "fighting words" based on some types of content but not others. In R.A.V. v. City of St. Paul, 505 U.S. 377 (1992), St. Paul passed a statute that said:

Whoever places on public or private property, a symbol, object, appellation, characterization or graffiti, including, but not limited to, a burning cross or Nazi swastika, which one knows or has reasonable grounds to know arouses anger, alarm or resentment in others on the basis of race, color, creed, religion or gender commits disorderly conduct and shall be guilty of a misdemeanor.

The Supreme Court struck it down saying:

Although the phrase in the ordinance, "arouses anger, alarm or resentment in others," has been limited by the Minnesota Supreme Court's construction to reach only those symbols or displays that amount to "fighting words," the remaining, unmodified terms make clear that the ordinance applies only to "fighting words" that insult, or provoke violence, "on the basis of race, color, creed, religion or gender." Displays containing abusive invective, no matter how vicious or severe, are permissible unless they are addressed to one of the specified disfavored topics. Those who wish to use "fighting words" in connection with other ideas — to express hostility, for example, on the basis of political affiliation, union membership, or homosexuality — are not covered. The First Amendment does not permit St. Paul to impose special prohibitions on those speakers who express views on disfavored subjects.