It all depends on the crab. There are definetly some which are not reef safe, but there are others that are consider fine. For the most part hermits, emeralds, and sally light foots are reef safe. I do know that even those crabs can cause problems with corals. I would say that hermits are usually a safe bet, but anything is possibly when it comes to crabs.
my sally light foot was fine until it got big, then it got too pushy knocking stuff over, and i had a feather duster kill'n peppermint shrimp..... my cleaners , camel back, arrow, emerald crab all seem to mind to themselves fine...