These days, a big act like that is like a freight train, and it takes awhile to stop it. You've still got stations playing songs because they're waiting to see if the negative reaction holds up, sales stats coming in from a week ago, concert ticket sales tallies that reflect transactions from last month at the latest, etc. We won't begin know the full extent of their career damage for several weeks. The thing to watch to find out if they've put a permanent nail in their coffin will be actual store sales of their next CD. Not units shipped to stores, but how many actually sell to customers. Even then, of course, you'll have the record companies trying to jigger the charts, and magazines like RS, with a vested interest in marginalizing the impact on their careers, playing down any sales slippage. But thanks to SoundScan, it's a lot harder to rig the record charts than it used to be.
By the way, I talk daily to radio DJs all over the world, and it's not just country listeners who are PO'ed at the Dixie Chicks, it's a lot of DJs and programmers, too. That is not a good sign for them.