Adding on to what 1848 said, Herefords have also been bred to now have about a 50/50 percentage of red/white necks, with some breeders focusing solely on one or the other.
The goggled-eyes on the Herefords has to do with preventing cancer eye, not pinkeye. Any of our cows with pigmented eyelids contract pinkeye just as easy as those who have white eyelids.
The two worst breeds for cancer eye are Herefords and Holsteins. The rate at which cancer attacks the eye in these breeds is determined by 2 factors: the strain of cancer and the inherited genetics. Cancer eye is believed to have a heridity factor of 0.4. Animals whose eyes bulge from the sockets are more likely to contract cancer eye, compared to those whose eyes rest normally in the sockets. Animals who have 'hooded' eyes (top of skull protrudes over the eye) can pass on this trait, are unlikely to contract cancer eye, and should be selected for this trait. Animals with white eyelids are more susceptable to cancer than those with a large patch of brown covering the entire eye area. If the animal has little pigmentation, it is more important to keep or purchase animals that have brown on the lower eyelid, rather than the upper eyelid. This is due to the angle at which UV rays hit the eye and the eyelid. The reason brown over the entire eye is preferred is because a cow's EYE is unpigmented at birth and becomes fully pigmented at an age of about 4-5 years. The amount of pigmentation deposited in the eye is directly correlated to the amount of pigmentation surrounding the eye. Therefore, brown covering the entire eyelid area results in cows whose eye's are completely pigmented when mature, lessening the chance of cancer eye.