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Now I have to go read up on why it looks different to different people. Maybe it’s something about different video displays.
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The photo as presented is blue and a dark neutral color.
If you look at the photo, the dress is in shade. There is also a bright and much different color light in the background which looks like direct sun.
Direct sun is a much more "yellow" color balance than shade, which is much more "blue".
If you put a white and gold dress in a shaded location with sun in the background, almost any camera's automatic white balance will key off the bright sunlight and everything in shade will appear blue.
The reason for the discontinuity is that your brain is trying to do automatic white balance of its own to try to analyze the photo.
It could actually be a blue dress. Or it could be white which appears blue due to the camera's shift in color balance. There's no way to be 100% sure without additional information.