''Wouldn't it be great if we could get them burning CDs and banning you from the radio?'' muses Dixie Chicks manager Simon Renshaw to the less-than-convinced country trio in the documentary Shut Up & Sing (R, 93 mins., 2006). At the time, news has just broken that lead singer Natalie Maines told a London audience she was ashamed that George W. Bush, then preparing to attack Iraq, was from Texas. We don't know for sure whether Maines & Co. subsequently made Renshaw write ''Be careful what you wish for'' a thousand times on a chalkboard. But had they done so, it would surely have been recorded in this authoritative film about the ensuing anti-Chicks backlash and the ways the band dealt with it. (Full disclosure: One of those ways was by appearing, naked and covered with slogans, on a cover of EW; a less-racy version of that photo decorates the DVD box.) Granted extremely extensive behind-the-scenes access, filmmakers Barbara Kopple and Cecilia Peck have crafted a great film about country music and an even better one about the country in which we live.