Do you feel you must must take your purse?
Others have said no one will touch your "stuff" and that's probably the case, but generally, when hubby and I go on snorkeling excursions, we take as little as possible. We have purchased "dry boxes" -- little plastic waterproof cases that have a cord so you can wear them around your neck. You can put your wallet in some of the larger ones, or the smaller ones will hold credit card/ID as well as cash and Sign and Sail cards. That way, the most anyone can abscond with are your towels and any clothing you've left under a palapa! (or maybe your camera if you haven't brought an underwater camera)
We've never had a problem with anything being stolen.....I don't know if we're just lucky or if that is the norm.