Answer:
Generally clays. Perhaps you've seen some makeup bottles labeled with something like "kaolin". "kaolin" is referring to kaolinite clay. I've also heard of montmorrilonite clays being used in makeup, but don't quote me on that. Another mineral group used in some makeup (mainly just glitter) would be the micas. Biotite is one, and Muscovite is another. They appear in sheets in nature, but are processed and used for glitter. As a sheet silicate, they readily separate and don't require much effort to break apart into specks of glitter.
Everyday Minerals uses Mica, Kaolin (in the Kaolin Powders), zinc oxide, titanium dioxide, and iron oxide. In the Finishing dust they do use zea maiz. The everynight minerals have caprylic and tocopherol. They also have a really great fan club that they have started, they are giving out really great gifts!