"Two men were killed Sunday in a Dallas suburb after they opened fire outside a building where an exhibit that featured cartoon drawings of Islam's Prophet Muhammad was being held, city officials said." - Nathan Koppel and Ana Campoy, The Wall Street Journal, May 4, 2014. Here is the article.
As experts in communications know: Humor is a subversive weapon. Use it with care. Also, it's subjective. What one person finds amusing, another can experience as insensitive.
So, no surprise, humor's risk frequently is perceived to outweigh its rewards. And, even cutting-edge marketing firms will not have it as part of a campaign. This usually isn't framed as a freedom of speech issue but what will be effective in messaging. In his prime Don Draper of "Mad Men" intuitively knew when to use humor and when to not take the chance.
The American Freedom Defense Initiative choose to embrace that risk. That was even though cartoons about Muslim beliefs incited a mass murder in Denmark.
In addition to humor, The American Freedom Initiative has attempted to use provocative advertising such as the controversial "Killing Jews is Worship that draws us close to Allah." It intended to run that campaign in New York transit systems. Initially a federal judge approved that as constitutionally protected speech. However, reports WSJ:
"But the board of the MTA [Metropolitan Transportation Authority] voted in April to ban political and other potentially controversial noncommercial ads on buses and trains."