some are reef safe, some aren't. it is a species dependent question. I have two reef taks, both have a mantis (G. smithii in my 8gal, O. scyllarus in my 60gal). All mantids are coral-safe. invert-safe is another story. small mantids aren't physically capable of killing thick shelled snails or conchs for example, but a large peacock mantis (O. scyllarus) could. there's also the tendency of peacocks to get this nasty shell disease if they are put under really strong lighting required in a sps reef. Then there's fish safe. again species dependent. And then just to complicate things further, it all depends greatly on personality as well... every mantis is different; some are born killers, others are spineless hippies.
...long winded answer: depends on the species and individual. If you're thinking about a mantis reef, think about what set up you want, then select a species of mantis that best suits it and you.