I have bad, bad, bad astigmatism, and without glasses, can't even comb my hair in the mirror. I have managed to get some pretty expensive contacts, and wear them from time-to-time... but I really shoot better with glasses.
I shot my recurve solely with sights until a couple years ago, and always lined up the string (rear sight) in front of my eye, over the sight pin. Something about the way I did it, I often touched my glasses lens with the string, and ended up with wax on my right lens much of the time.
Now I shoot without sights, and cant the bow a little, and I don't touch my glasses lens anymore. I have no problems shooting with glasses, except for the fogging up, and occasionally having issues with peripheral vision (when seeing things outside of the lens).
Due to my heavy prescription, doctors have had a hard time correcting me to 20/20, and at different times in my life, different eyes have adapted to the best level of correction. The result is that I have no dominant eye... just the one I see better with at any given time. And now, with glasses my right eye sees best, and with contacts, my left sees best. When I switch between the two, it really throws a monkey wrench into shooting a bow!