There is a stigma against Herefords in my area because of cancer eye and I am very frustrated that the breed establishment has done nothing to address the issue. DNA samples have been collected for more than 15 years and not even the President of the American Hereford Association has any clue what has become with that line of research. Even if there isn't a simple genetic relationship, we should still have some guidance about how to breed away from cancer eye.
For the traditional authentic Hereford to have a place in the competitive marketplace, we need to with DNA be able to assure our customers that they will not have to deal with the stereotypical Hereford faults.
A storey is that HOPs with dark coat round their eyes are less prone to eye cancer. Makes sense to me, since cattle with white round their eyes are generally more prone to eye cancer. I favour that trait, as do some other HOP owners.
We definitely have the technology now to look for DNA differences. The problem for us would be getting samples. We haven't seen it in our Traditional cattle (yet). There are a few things however that we need to look at that are regarded as undesirable "Hereford traits". In UK the main criticism is lack of milk, although it is all relative and I think the Traditional population is not bad for this nowadays. Vaginal prolapse in another thing I've heard talked about but again I don't know how widespread it is - probably only seen in older cows? Udder conformation is very variable too, some being excellent and others not great, but it would need a lot of data collecting to make any judgements.
I have no reason to believe that the genetics behind cancer eye is unique to the American genepool. Being in a dry sunny climate exacerbates any genetic predisposition to eye issues. If I were to guess I would expect that around half the breed would have a genetic predisposition to cancer eye. One advantage that the OP Herefords have is that they are largely derived from older cows that have stayed in good health.