Long-time New York Times columnist Clyde Haberman has probably the best write-up of the Sharpton-Delonas-chimpanzee dust-up and reminds readers of something called the First Amendment. An excerpt:

The protests continue, though. Certainly, everyone has a right to refuse to buy a newspaper. But Mr. Sharpton has gone further. He wants the Federal Communications Commission to re-examine waivers to its media ownership rules that allow Rupert Murdoch to own two newspapers (The Post and The Wall Street Journal) and two television stations (WNYW and WWOR) in the New York area.
Normally when it comes to such waivers, the question is whether a single hand controls too many media outlets in a given market. But Mr. Sharpton has made editorial content the reason for asking the government to step in. “How can you continue to have these waivers,” he told a CNN interviewer, if you “don’t understand what would offend a large amount of African-Americans — and whites, by the way?”
THUS did he take the first step down a very slippery slope. The First Amendment protects even the most despicable form of expression from government interference. It is why the Supreme Court has upheld the right to burn an American flag even though flag desecration is as offensive to many people as Mr. Sharpton says this cartoon was to him.