At the end of the day, it amounts to whether you consider it to be persecution or not. If a radio station says "they're un-patriotic, we wont play their records" is that persecution? If there are people out there who'll turn off the radio as soon as the Dixie Chicks come on (cause they're anti-war as opposed to the correct answer "they suck") then the radio station has got to see them as a liability, and therefore has no right to keep them on their playlist if they'll decrease listeners. However, to say, out and out, that pro-peace = anti-american, thats stupid. Its like saying pro-abortion = anti-life.
On an unrelated note, i think that the Dixie Chicks/ Michael Moores comments will boost their career rather than hinder it. The majority of people in 1st world countries are anti-war, even if America generally isn't.
Personally I'm British. Here you get persecuted for saying Bush is right to go to war