I've lived in Ireland and the UK which have a big drinking culture. I have heard a few people say that not consuming alcohol carries a stigma but I don't know whether I'd agree with that. Sure, people may look at you as bit weird but I don't think the stigma compares to drinking excessively or even being an alcoholic.
My sister is a therapist who worked with teenagers told me that several girls and boys she knew had a parent(s) who consuming excessively and some even during the day. Most of them never made a fool of themselves but the teens were always embarrassed having their friends come over and hang out if the parents were drunk. Conversely, I had parents who never drank and was comfortable sharing it with friends/coworkers.
I think alcohol is acceptable depending on the set/setting and showing a dependence on it is still very much stigmatised moreso than not drinking at all.