The human visual system's tendency to perceive an object's colour as relatively stable even when the lighting around it changes.
The brain partially compensates for changes in illuminant colour temperature so that a white object still looks roughly white under both warm and cool light — this compensation is imperfect and varies between observers, which is part of why people can genuinely disagree about what colour something (including an eye) looks.
Colour constancy is a perceptual/brain effect, not a property of the object itself — it's a different phenomenon from metamerism, which is about the physical light reaching the eye rather than how the brain interprets it.
Two observers looking at the same eyes under the same light can genuinely disagree on whether they read as green or hazel, partly because of individual differences in colour constancy.
Explains why eye-colour classification is inherently somewhat subjective, even before cameras and photography are involved.