Sulfites occur naturally in some foods. They exist in fermented products such as beer and wine as they are produced by yeasts in the fermentation process. Additional sulfites or sulfur dioxide is commonly added to wine to prevent oxidation and bacterial activity. That is, to preserve color and taste. Since July 1987, the U.S. government has required the sulfites warning label on all alcoholic beverages with at least 10 parts per million of sulfur dioxide.
Organic wines have sulfites.
In other words, if you're drinking wine, you're drinking sulfites. That's just the way the cork the crumbles. But it's not just wine. The FDA warns of sulfites because a portion of the population is sulfite-sensitive. That is, they may suffer an adverse reaction to sulfites.