So we're going with sulfites this time around instead of sulphites.
Sulfites have been used in wine making for centuries, probably even before academia could explain what was going on chemically. The same with food. Let's not forget that sulfites occur naturally in soil also, so really nothing coming out of the ground is immune to the sulfite charge.
As stated previously, wines typically may contain 350ppm in sulfites. Per the USDA National Organic Program 100ppm becomes the new cut-off for organic labeling. (In fact most such wines are in the 40-80ppm range.) Also no added sulfites are permissible in the USDA organic program. In order for a "No Sulfites" label to be legit, the wine must have less than 10ppm in naturally occurring sulfites. These standards are set by the USDA for both domestic and imported wines.
Worldwide the "organic" wine label applies to the farming of grapes only. Only natural farming methods are allowed which precludes pesticides, herbicides, chemicals, fertilizers, or insecticides.
There is a simple way to remove sulfites from wine according to winefolly.com. Add a few drops pf hydrogen peroxide to your glass of wine and that should do the trick. Or if that's too gross there are somewhat pricy commercial products on the market that will do the same thing but those products are just made up of hydrogen peroxide and water.