You can touch most corals with bare hands. Some people a precautious about zoos. But I dont think crabs or hermits would harm the sun coral. Especially shrimp too. They dont harm coral for the most part.
Misconception. True, hermits do not directly harm sun corals, nor do shrimp. However over time the hermits/shrimp will learn that the sun coral eats the same food that they like to eat. So when it's feeding time eventually they'll go over to the sun coral and rip the food out of its mouth, eventually starving it to death...
As for handling corals, the two most common difficulties are dealing with the nematocysts of LPS and the toxins of zoanthids/palythoa. LPS have stinger tentacles with whar are called nematocysts. Their tentacles are lined with lysosomes (little cellular structures) that have hooks on them (like microscopic fishooks). They literally stick to your finger and release the enzymes in the lysosomes on to your finger. These lysosomes have enzymes and chemicals that some are allergic too and over-time if you leave it there, they will eat away your fingers. Now that I've scared you, so long as you're not allergic these really aren't that big a deal. You can touch them with your fingers and be OK. REALLY sticky corals might be irritating, but likely won't hurt you too bad.
Zoanthids/Palythoa are a different story entirely. They have a toxin in their flesh called Palyotoxin. Its an exceptionally powerful toxin that targets nerve function. It can NOT however be absorbed through the skin. It needs a mucous membrane pathway to get into your system (eyes, nose, mouth, open sore, etc). Once in your system, palyotoxin in small doses will numb the area of contact, and inhibit nerve funciton there. This is a common difficulty if you're handling zoas/palys and decide to scratch your eye/lip/etc. Whoops, now the whole side of your face is numb for a little while
. There are also a small portion of the population again who is allergic to palyotoxin, so anaphylactic reactions are possible.
Solutions: Wash your hands and don't go around touching other things right after you touch corals. Proceed directly to the sink, do not pass go do not collect $200. It is also important to note that palyotoxin can stay around for days even when dry, so don't go rubbing your face with the towel you dry your hands with
Edit: If you ever do experience an anaphylactic reaction from contacting anything in your aquarium, make SURE you tell the paramedics or whomever calls them that the source of the reaction was a coral from your aquarium. Will help with treatment if there is a problem