They weren't. The complaint about the war wasn't from the standpoint of centrist criticism regarding its necessity. It was from the lefty standpoint that it was "racist" (lol) and "violent". At no point did Natalie Maines articulate a reasonable case against the Iraq war which would stand up either then or today.
The removal of "Dixie" from their name pretty much says it all. Dixie itself does not have a negative or racist connotation. It's not like times have changed, and their name had become representative of something bad. Dixie simply meant "the southeastern United States". They equated it with a term for the Confederate Army, which is not true. It is a much broader term describing the region. They just became afraid to be associated with an area of the country which became dark red politically, and used the "slavery" thing as an excuse to drop that from their name.
Also, their feud with Toby Keith was ridiculous. Their issue was with his "Red, White, and Blue" song, which was clearly about getting retribution against the 9/11 terrorists. They lyrics made that extremely clear, and there was absolutely nothing racist or Islamophobic about his song. Despite that, Natalie Maines made a huge deal about it, calling the song (and Toby) "ignorant", and various other names. Then, when Keith responded explaining himself, Maines wore a shirt reading "FTK" at the Country Music Awards, which stood for "Fuck Toby Keith". When questioned about it, she lied and said it was "Friends for Truth and Kindness", and only later admitted it really meant Fuck Toby Keith.
Fuck Natalie Maines and the Dixie Chicks.