Most puffers will at least try any coral (or live rock) put in the tank at least once. They explore things by biting. Mushrooms they will leave alone after the first bite. Most soft corals except for star polyps seem to taste nasty to my blue spot toby - he has tried all of them but only ate some of the polyps. Found that if you feed at regular times and have a few cheap snails or hermit crabs in with a puffer, they leave the corals alone (well mine does).