Since those differences in the properties of the eye are compensated through experience and interaction with the visual environment, it is unlikely that they can explain the differences in perceiving the colour of the dress in that photo.
Conway thought the reporter was exaggerating, saying, "I didn't appreciate the full extent of what was about to happen. The light hits the retina in the back of the eye where pigments fire up neural connections to the visual cortex, the part of the brain that processes those signals into an image.
In reality there is — most of the time — sufficient information about the illumination that allows for separating both factors, surfaces of objects and illuminations.
In particular, the colours in that photo do not appear like illuminated surfaces in a real scene, but like a self-contained, artificial configuration of colour patches.
The third set of colours. What is the real colour of the dress? Irreversibility of interpretation. In another, it looks yellow-white.
Meanwhile, when Conway woke up the next morning, his inbox had so many emails about the dress that at first, he thought his email had been hacked, until he saw that the bulk were interview requests from major media organisations.
Apart from the eye, the brain plays a major role for enabling perception. At least we can all agree on one thing: The people who see the dress as white are utterly, completely wrong.