Sure they do.
Carrageenan is a natural emulsifier. Probably more "natural" if you just boil the seaweed it comes from and not put it through a lot of chemical processing steps. Guar gum is natural, it comes from beans; lecithin is natural, it comes from egg yolks.
If you look around your environment, there are probably many plant products that can be used as emulsifiers, you just aren't going to find much emulsifying potential in the pure waxes and fats that you mentioned. Many beans contain natural emulsifiers. A good chunk of the soybean crop is converted into soya lecithin that is used as an emulsifier. I'm personally familiar with the emulsifiers in
palo verde beans. When beans have too much natural emulsifier in them, some people find them objectionable and they think less of them as a food source. The same is true of okra.
Here is a page from an herbalist claiming to make creams "without emulsifiers", but then they use aloe -- which is another natural emulsifier.