I recently was playing missions with a friend. We are both playing Charr but have been picking different paths. When it came to choosing which order we picked different also. I picked the Order of Whisper and he chose the Order of Vigil. When playing the next mission it asked if I wanted to continue my story at the end his (it was the meeting in LA). I figured it was just a cut scene more or less so I accepted. After it changed my order to Vigil instead of Whisper.
From what I understood once an order was picked it was permanent. As of now I can see no way to change back.