OGWA allows for sulfur dioxide treatment of wines as long as the resulting level of sulfites in any wine does not exceed 100 ppm. It is simply that sulfur dioxide inhibits growth of molds and bacteria and stops oxidation. For organic wines, the presence of this warning will mean that the wine has between 10 ppm and 100 ppm of sulfites. If you are sulfite-sensitive, you will have to make a judgement on the wines you can drink. The number of certified organic beers available in the U.S. is not large.
Domestic examples are very few.
The list expands slightly when we look at some Belgian, French, and Scottish offerings. Some very good examples of these are readily available in the Chicago area. As of this writing, none of the brewers in the Chicago area is making a certified organic beer. The most readily available, relatively local organic beer comes from Lakefront Brewing Co. in Milwaukee. Lakefront has also recently released an anniversary barley wine, Beer Line Barley Wine Style Ale.