If I were the State Department, I would develop a brutal sense of humor. I would focus that sense of humor, not on religious icons, but on leaders. I would lampoon those leaders in a way that nobody in the society is allowed to do. I would empower the people by being their voice by proxy. I would eliminate fear by laughing at it.
Underneath it all would be the message of freedom, because we do what they are unable to do for themselves. When the propagandists are wrong, make fun of them for it. When they are right, make fun of them for it. When they are silent, make fun of them for it.