I agree with Jimmy that they are reef safe. I don't recall ever seening one that had a large enough mouth to eat a grown Lysmata though. I find smaller fish like flame hawks and psuedochromis are a much greater threat to your shrimp population.
They have a nasty tendency to eat fleshy LPS (open brains, scolymia, elegance) as well as euphyllia. I get lots of them traded in for this behavior.. I don't consider them LPS safe at all.
I say they're reef safe. Have had one in my 180g reef with no problems for 3 years. It's never touched any corals, but a 56g tank is too small they grow fast and get pretty big. Mine is now over 7" and it was only about 2" when I got it.
My Foxface has been no problem around Inverts and Mushrooms. Very nice fish and grows fast. Mine is now very happy in a 100 gallon. They need lots of Veggies. I give mine Romaine and Spinach at least once daily and also feed chopped shrimp and fish from the grocery store. Rabbit eats out of my Hand but I don't recommend you doin the same.
I had one a few years ago that was harmless. Fish was always out and swimming around. RIP, it jumped and got stuck in my Durso standpipe.
I got another one about a month ago. I hardly saw the thing, it was always scared and after 2 days of it in my tank I never saw my 2 year old cleaner shrimp. Anyway, I haven't seen the foxface in 2 weeks now, so I think it is a goner.
_________________ grand daddy purple strain