The base recipe for a sorbet is normally sugar water and fruit puree. Sorbets can also be made with juices or beverages like herbs or tea. The main cause of the "icy" texture is the high water content. To avoid that, you don't necessarily need a thickening/emulsifying agent (rather than a stabilizer per se). Normally those kind of additives are put in the base recipe to avoid the splitting of the sugar that may occur if the sorbet is kept for a long time, especially if it's made with a really watery juice (as lemon for example). On the market it's possible to find some sugar syrups made specifically for sorbet that contains pectin.
But even with a thickener introduced in the recipe the main things that keep a sorbet smooth and airy are sugar (for its anti-freezing properties, the higher the sugar softer the end product will be) and the air that gets incorporated in the sorbet during the mixing in an ice cream machine. Plus the trick to the perfect ice cream or sorbet is to mix it in the ice cream maker until it feel "dry" to the touch, this way it'll keep the proper texture longer.