It’s okay not to drink. No one so far has said anything to me about it if I don’t. However, if you want to anyway (and occasionally I do want to try something new), my suggestions:
Hard cider and Zima have about the alcohol content of beer but taste very different; you might like them. If you’re at a brewpub, ask if they have anything which isn’t hopped or is EXTREMELY lightly hopped and try that. Failing that, try things with interesting names and hope for the best. I don’t like most beers, but I can generally tolerate Sam Adams or Anchor Steam (the colder the better in both cases).
I do like some wines, so without knowing exactly what you don’t like it’s hard to offer suggestions.
Some people don’t like dry wines. “Late Harvest” or “Eiswein” or “Botrytised” wines tend to be sweet and don’t have the same social stigma as, say, Boones Farm Strawberry Hill.
Some people (me, for one) don’t like tannins. Shelf talkers or a knowledgeable friend can help you out here; if you hear the word “oak” stay far away from it.
My suggestions: Zinfandel, Gewurtztraminer.
Also, if you can find a varietal with “Chaunac”, “Concord”, or “Catawba” in its name, give it a go; if nothing else it’ll be different and will give you an excuse most places (“Do you by any chance have Ferrigno Blanc de Chaunac? No? How unfortunate. Iced tea, then, I suppose.”).
If you’re fortunate enough to live near a vineyard you can usually taste several of their varieties either free or for a small fee and find something you like this way.