Well, even if it was true that right-wingers never compose songs /maybe they just neglect this mean of persuasion/ there were moments in history when part of conservatives and extreme leftists strangely unite for a common goal. The most exclusive case was isolationism movement short time before WW II in the U.S. There was a famous group named Almanac Singers, who made full album named Songs for John Doe, expressing not pacifism, but extreme willingness to avoid war at any cost. One of the songs has a chorus: "plow under... every fourth American boy!" Which was taken out of of the speech of famous pro-Hitlerite Charles Lindbergh, isn´t it?
And what about Barry Sadler and his "Universal Pacifist"? Sorry, can't remember the full text now, but the message is: "He doesn't have the courage to be free".