My total lifetime alcohol consumption, excluding medications, has been about 3 sips of champagne and maybe 1/4 glass of wine, so I guess I qualify.
In my case, there are many alcoholics in my family: having seen the damage it causes and given the potential for a genetic predisposition to the disease, I decided it wasn't worth it.
As for dating, my preference is women who do not consume alcohol at all; I doubt I would consider anyone who drinks more than a very limited amount on an infrequent basis. As William noted, alcohol consumption itself is not an inherent moral concern (although it can easily become one); however, there are a variety of practical considerations I'd rather avoid entirely.
As for finding women that don't drink at all, that is a big bonus to come across. I have however always struck out on said women. Even with that one big piece fitting, all the other pieces need to fit to complete the puzzle.
However, I dont really know why a woman would hold the fact that you dont drink against you. And if she does, well then, you and her obviously arent a match, so just move on to the next one. As for social occasions and friends, I am sure you could find plenty of people that dont drink, that you could hang out with, if you are finding that going to bars just isnt any fun for you.