They will argue the person on-the-air has the right to say what he/she wants and if you dont like it, just go away.
Unfortunately, this argument does not stand up to the legal realities concerning the public airwaves.
All radio stations (and Im referring to the United States) are licensed on behalf of the public to licensees (station owners) who agree to run these radio stations according to the laws in place.
According to the Federal Communications Commission:
It is a violation of federal law to broadcast obscene programming at any time. It is also a violation of federal law to broadcast indecent programming during certain hours. Congress has given the Federal Communications Commission (FCC) the responsibility for administratively enforcing the law that governs these types of broadcasts. The Commission may revoke a station license, impose a monetary forfeiture, or issue a warning, for the broadcast of obscene or indecent material.
Obscene Broadcasts Are Prohibited at All Times
Obscene speech is not protected by the First Amendment and cannot be broadcast at any time. To be obscene, material must meet a three-prong test:
1. An average person, applying contemporary community standards, must find that the material, as a whole, appeals to the prurient interest;
2. The material must depict or describe, in a patently offensive way, sexual conduct specifically defined by applicable law; and
3. The material, taken as a whole, must lack serious literary, artistic, political, or scientific value.
Indecent Broadcast Restrictions
The FCC has defined broadcast indecency as "language or material that, in context, depicts or describes, in terms patently offensive as measured by contemporary community broadcast standards for the broadcast medium, sexual or excretory organs or activities." Indecent programming contains patently offensive sexual or excretory references that do not rise to the level of obscenity. As such, the courts have held that indecent material is protected by the First Amendment and cannot be banned entirely. It may, however, be restricted in order to avoid its broadcast during times of the day when there is a reasonable risk that children may be in the audience.
Consistent with a federal statute and federal court decisions interpreting the indecency statute, the Commission adopted a rule pursuant to which broadcasts -- both on television and radio -- that fit within the indecency definition and that are aired between 6:00 a.m. and 10:00 p.m. are subject to indecency enforcement action.
Indecent Broadcast Restrictions
Enforcement actions in this area are based on documented complaints received from the public about indecent or obscene broadcasting. The FCCs staff reviews each complaint to determine whether it has sufficient information to suggest that there has been a violation of the obscenity or indecency laws. If it appears that a violation may have occurred, the staff will start an investigation by sending a letter of inquiry to the broadcast station.
If a complaint does not contain information sufficient to determine that a violation may have occurred, the complaint will be dismissed. In such a case, the complainant has the option of re-filing the complaint with additional information, filing a petition for reconsideration of the staff action, or filing an application for review (appeal) to the full Commission.
If the facts and information contained in the complaint suggest that a violation did not occur, then the complaint will be denied. In that situation, the complainant has the option of filing a petition for reconsideration of the staff action or an appeal to the full Commission.
- portions of the above directly from the F.C.C. website

