I can only see it as blue, period. Not trolling - I really cannot see this as white in any circumstances, even the XKCD "color balanced" bit I still see it as blue (albeit a much lighter blue on the left).
When I looked at the image, I saw a bluish and brownish dress.
In the XKCD image, I can say that they are both blue in color, with the dark room one being lighter blue in appearance to my eye, yet I know my interpretation would be more that it was in fact a white dress in a darkly lit area.
I have sunglasses that are brown tinted, and technically everything I see with them on has a brown tint to it, yet I know my brain is ignoring this (unless I am really thinking about it) and perceiving the colors for what I know they are. Your brain does an incredible amount of processing and interpretation of the things you see.
On reviewing the image again, I can see the over exposed background which does suggest the exposure of the dress itself is darkened, and therefore is white, or at least much lighter than it appears in the image.
I am reminded of this as well: