Anemones should be fine.
What type of montipora?
Usually the least safe corals are polyps (zoas, button polyps, goniopora aka flower pot coral, pagoda cup, star polyps) basically the more it looks like a plant, the more likely they are to eat it.
A lot depends on the fish, some prefer SPS polyps, some only eat zoas. My dwarf angels don't eat coral, but my friend has a flame that destroys her acans.
I would say torches, frogspawn, hammers, and bubble coral are pretty safe, still a risk. Bubble coral has the harshest sting, so that to me would be a good one to start with.