Put simply, if there's something that you'd be leaving in your room that would be tragic for you to lose, don't bring it. And if you're not comfortable leaving those items at home in an empty house, leave them with a trusted friend/neighbor who will be home.
My rings are the most precious things to me, but I never take them off except to clean them. I bring my diamond stud earrings and lock them in the safe when not wearing them. And if they get stolen.... well... life goes on.
Things are THINGS.
P.S. Have never had anything stolen out of our room or room safe in Playa, whether AI or non-AI. Once we left our backpack at Carlos & Charlies (after waaaaay too many margaritas,) and the waiter caught us just before we walked out the door.