Are reddish egg whites safe to eat?
Intact and good-looking eggs are generally safe to eat -- any spoilage very quickly results in horrible smell. The thing you're seeing might actually be a very tiny remain of something related with embryo (there's a tiny red piece of embryo in all eggs, you just have to search a bit) or a colored piece of internal egg-white structure (I heard that grass- and mineral-rich food may cause coloring like that), just bigger for some reason.

Anyway, I'm regularly eating eggs like that since childhood and I'm still here. It's safe.

(PS. I never tried to drink anything like this uncooked, but there are many other reasons not to try that. :D)