I'm curious if the coloring for the outfit looks as expected when you are in a conversation. We are looking into this issue and any information can help us track down what is occurring. The details already provided have already given us some excellent leads and we hope to get this all sorted out quickly.
This has been a problem on my blue Twi'lek character Da'ru with the Slave Outfit, the Republic Dancer's Outfit, and the Black Hole Force-Mystic/Campaign gear (which can appear from almost completely white to pure black on different characters when outside of a cutscene). I've reported it several times over the last year, including submissions w/ screenshots of my character compared to other characters. >.<
From my observations, it seems to be that the darker the skin of your character, the lighter the textures on the affected clothing will be.