The adhesives used on fruit stickers are regulated by the FDA as "indirect food-contact substances," says Soo Kim, a spokesperson for the Department of Agriculture's Agricultural Marketing Service. (The ingredients that may be used are outlined in the Code of Federal Regulations part 175.125.) The same rules apply to adhesives for both organic and nonorganic fruit, says Barbara Haumann, a spokesperson for the Organic Trade Association.
So the glue isn't necessarily organic, but could it contain any animal products? It's possible, but unlikely. "Although adhesives made from animal products would not be prohibited, most of those that are specifically approved for this use [on fruit stickers] are not formed from animal products," says Doug Karas, a spokesperson for the FDA.
Karas says that for any food-contact substance to be approved, the FDA considers its composition, the amount a consumer might eat, short- and long-term health effects, and any other safety factors. The FDA then sets a threshold "much lower than what would be expected to have any adverse effect." Still, Karas says, "whether there are labels on fruit and vegetables, we would advise anyone to wash produce before eating it."