E1556 | play | medium | “Emerald ID: E1556 – Weight: 1.43 Carats – Origin: Colombia”
Hand sanitizer cannot damage emeralds, but might be able to damage its oil filler.
Emerald in general is a very durable stone. It is scratch resistant, tough enough to withstand being worn on your finger on a daily basis, and is resistant to most chemicals and light (including UV light).
The only issue most people have with them is their clarity. Vendors and sellers treat emerald’s clarity by oiling the emeralds.
Due to their high number of visible fractures over 99% of emeralds are treated for clarity, usually with oil. Cedar oil is used because its refractive index is very close to that of an emerald, meaning light passes through the oil and emeralds very similarly.
There are other treatments, like resin, but when it dries out it cannot be completely cleaned and removed from the emerald (though there are places that claim to be able to do it with a special formula). Oil is relatively easy to clean out and reapply, even if it dries faster than resin or gets damaged by mild house-hold chemicals (anything safe for your skin is not that damaging). It does require some heat and pressure, meaning it’s not something you can DIY.
The oil used is also a specific type, not the cedar oil used in incense burners and furniture polish.
In the same way that hand sanitizer can leave your hands cracked, most hand-sanitizers will dry-out the oil in emeralds too with repeated exposure and application. This is due to the alcohol ingredient, which is the main ingredient in most sanitizers, soaps, and a lot of other cleaning detergents. Limited amounts of exposure will not dry out the oil though.