When you say don't drink, do you mean you don't like to drink alcohol, or you don't like licensed venues at all.
I'm by no means teetotal, but when out I tend to stick to non-alcoholic drinks, it doesn't effect my social situation at all. If I decided I didn't want to enter any pub or bar, that would affect my social life though.
I may be wrong, but from the outside it looks like some societies associated with sports may place more emphasis on alcohol, but your mileage may vary.