I think this whole phenomenon is a great example of how different brains approach a seemingly straightforward task.
This is how I take this:
GOLD & BLUE
Their brains are asking “What wavelengths are hitting my retina?” I think the literal color of the pixels on the screen (as supported by @ragingloli example using Photoshop) are gold and blue.
GOLD & WHITE
Their brains are asking “What wavelengths are hitting my retina and what does this mean?” I would bet that most people in this camp can see the blue/white. But are making the actual decision to adjust to white.
BLACK & BLUE:
Their brains are asking “What color is this dress?” Their brains take in the overexposed background and adjustments are made on a subconscious level.
To put in relation to photography…
GOLD & BLUE: shooting in RAW
GOLD & WHITE: shooting with some manual settings
BLACK & BLUE: shooting on auto
Especially in relation to what @janbb referenced, it’s incredibly fascinating! Challenges what people think of as matter of fact.
I wonder how the BLACK & BLUE group would respond to the image cropped from its background?