Known Predators or potential predators:

Sundial SnailConsumes zoanthids.
Zoa-eating Nudibranchconsumes zoanthids, takes on their color pigment and blends in to continue the damage.
Zoanthid Spiderpreys upon Zoanthus sp.
Aiptasiastings corals to gain space. Can sting seahorses.
Juvenile Blue Angelbasically not reef safe; will damage most corals, sponges, and inverts.
Regal/Hippo TangChews up zoanthids, for no good reason. May assist with algae control.