I think to the Left, of which the Dixie Chunks are evidently a part, when they talk about closed minds, they are talking about people who believe in certain absolutes. Leftists pretend that everything is grey, IMO, because they wish to destroy our American traditions of individual freedom so they can substitute their egalitarian communism or socialism.
So, yeah, great point, it is good to have our minds made up on certain things, even if that means the Left refers to us as "close minded."