To answer your question, they can straight up kill/eat/destroy coral and inverts. Given the research I've done, I don't think it's that common, but I've experienced it first hand.
I really enjoyed my cleaner shrimp...at first. They are a beautiful addition to any reef tank, especially when their antennae get longer, and they are great at cleaning up excess food. However, mine has been a terror to my corals and feather dusters for months now. He's completely eaten the head off of a large Hawaiian feather duster that I've had for over a year, and he's currently been attacking my coco worm and duncan coral. In the past he's also eaten parts of my stylophora, so it's definitely not just LPS that he goes after.
And this is not speculation either. I have 100% witnessed him eating these first hand. Some people will say: "Oh, hes was just eating dead tissue or algae off the coral" or "You're not feeding him enough". No. I've seen him cutting polyps off of my stylo and eating them. I've seen him devour my feather duster. Just an hour ago I watched him trying to get at my coco worm deep in his cocoon even after the worm had retracted. I've tried spot-feeding him, over-feeding the tank, etc and he still goes after them. As soon as my QT tank is cycled I'll be removing him to give to another local reefer and in the future I'm not sure I'll ever have them in my tank again. Perhaps a much larger tank, but realistically that would just make him harder to catch.
I'm all about having a full ecosystem in my tank, and I can certainly take the good with the bad. I've dealt with my pistol shrimp burying corals, my pincushion urchin moving corals, my bicolor blenny camping out on my zoas keeping them closed, but when it comes to an inhabitant straight up eating my corals, I draw the line. Not nipping. Not irritating. Consuming them. To the point where if I don't intervene they will not survive. I'm pretty sure my feather duster won't be growing back, but I'm giving it a chance and hoping for the best as it was one of my favorite tank inhabitants.
Again, I don't want to scare you as I don't think this is that common, but don't believe for one second that cleaner shrimp are 100% reef safe, as I can tell you from experience they are not.