Any Mediterranid society with a light-eyed minority and dark or mixed-eyed majority could discriminate by eye colour in this way - and did in history. The superstition of the 'evil eye' is strongly linked to the notion that people with blue or green eyes cause or propagate it; in modern-day Greece and Turkey amulets against the evil eye still take the form of a blue eye, intended to counter the blue-eye matiasma.
You could also have prejudice against recessive genotypes, fuelled by a form of eugenics. The argument goes that recessive genes behave the way they do because they are damaged - when the body has a damaged and a healthy gene to choose from it expresses the healthy (dominant) one, but when both copies are damaged (i.e. recessive) it has no choice but to express the recessive phenotype.*
Adherents to this philosophy could appeal to the fact that blue eyes confer no known survival advantage (indeed, slightly reduce vision in bright sunlight) and are likely simply a byproduct of more advantageous pseudo-albinism in colder climates. Of course, such a view would likely only take off in a society where most people had dominant hair/eye genes and the 'inferior' type was a minority.
Obviously, if you want prejudice against blue-eyed people to remain to the present day you need nations without a sizeable plurality of blue-eyed people to predominate. That's obviously easy to do in a world where the major world powers are, say, Chinese, Turkic, or Indian. OP mentions 'Western society' and implies it would just be blue eyes that were the subject of prejudice, so you're best off with Mediterranean powers retaining their dominance somehow (a hard sell given the lushness and rich mineral resources of northern/western Europe once it's civilised). A surviving Roman Empire is probably too late, since IIRC light phenotypes were already considered attractive, albeit somewhat exotic.
* Of course, this is nonsense, as the process of meiosis does not automatically know what traits will be advantageous in every situation and environment. A gene could be 'damaged' as far as the genome's 'antivirus' is concerned but still offer significant advantages, which is of course how individual mutations become widespread genotypes in the first place. 'Recessive' and 'dominant' are of course relative - if a recessive gene manages to completely elbow out a dominant gene from the pool with its survival advantages, then with nothing dominant to it, it becomes the most dominant gene for that trait.