"Dixie" was the battle song of the separatist Southern States in the failed American Civil War. If you whistle Dixie you are singing the battle cry of the side that lost, a useless act. If it is said that you are not whistling Dixie then it means that there is validity to what you have said or what you are doing.
Put another way, you are not (whistling Dixie) wrong.
- For Teachers