Hello, This bug actually was one of (the many) reasons why I stopped playing the game. I've added a link to video "evidence" of the bug happening. Also you can "fix" this out of combat when you respec your talents and spec back again altho it only works until the BD in your party (supposedly) bugs it for you again.
Just as soon as I hit lvl 4 and selected a faction I wanted to test it out so I put on the costume killed one guy and left the area. About 15 minutes later I noticed that the faction battle music is still on even though I changed the pvp-costume to a non-pvp one already. Had to relog to make it stop since changing loop or faction music in sound options didn't help.