How strictly is the "no dogs on beach" law enforced in Florida?

My hubby and I are (were?) planning to spend 10 days in the Florida Keys at Christmas. In researching RV camps all of the ones I've looked at so far accept pets, but they have a statement re Florida law prohibiting pets on beaches. Is this law 1) for real? and 2) strictly enforced? I realize service dogs are not included in the exclusion of pets on beaches, but I'm thinking I'm not going to Florida if I can't take my strictly pet dog with me.