As a Kansas criminal defense attorney, I have had numerous cases where my client was being prosecuted for getting too rowdy or yelling profanity. They get charged with the ambiguous disorderly conduct. That's when a Constitutional argument over the First amendment is in order.
During the seventies, the United States Supreme Court Supreme Court clarified that profanity, as part of a political message, is Constitutionally protected speech. In Cohen vs. California, the Supreme Court stated that it was Constitutional for a person to walk through the courthouse wearing a jacket that said "Fuck the Draft." However, there have been other cases where, the Court seemed to indicate that some profanity could be prosecuted, if it wasn't specifically connected to a political message. Even so, the Court has overturned convictions and allowed profanity even when not connected to a specific message. In those cases, the Court said that the governmental intrusion wasn't allowed because they had not met its heavy burden of showing how protected speech would be honored and there would be no chill factor. The reality is, that it is unlikely that the government could both write law prohibiting profanity, while at the same time relying how speech wouldn't be curtailed.
Interestingly, the Supreme Court has upheld regulation against profanity on broadcasts like radio and tv. When it comes to the internet, more freedom is allowed. When the Supreme Court ruled unconstitutional, the Communications Decency Act, in 1997, it stated that you can be indecent, but not obscene… whatever that means.
Individually, I rarely swear and generally try to speak in an uplifting respectful manner. However, in the United States of America, I would support someone else's right to free speech, even if I disagree with their message or even the profanity they may use to express it. As a lawyer who has seen the government in action, I am wary to entrust the government to tell people what they can or can't say.
One extreme example would be the deceased Fred Phelps. Personally, I feel that his speech is deplorable and sick. However, I would support his right to free speech. If you support free speech, you can't pick and choose what should be protected based on what speech you agrre with individually.