Tim, I rarely have any problems with pinkeye. One last summer that vet treated on his regular visit in July. I can't remember when before that.  My cattle get a pinkeye shot annually.   My vet said that he sees more pinkeye in many black Angus herds.  I feel pink eye is more about fly control and flies carrying it from neighboring herds than it is about breeds.  Cancer eye is another matter but that has been pretty much bred out of Herefords. Eye pigment helps. Most of my Herefords have at least some eye pigment.