Originally Posted by
Acheleus 
It bothers them that I don't drink.
I bet it doesn't bother them as much as you think. We think everyone notices things, judges them, cares about them- they really don't. Especially if you are newly getting to know them and they don't know you are an alcoholic, I would wager big that they just don't think about it or care much. If they do, or are nosy, shut them down politely and move on with getting to know them safely, for you- I bet the "issue" is a non-issue soon, if it ever was. Especially as you said their drinking is not how yours was- normal drinkers don't think about alcoholic drinking behavior because it isn't their focus.
Hang in, don't go with them, or go infrequently, tell white lies about why you aren't drinking if you need to - whatever it takes to stay sober. One year, right?! Do not risk losing that over this or them.