Back to the original question: The one fruit in my yard that is never molested by any mammal, bird, or insect is the Thai Giant Jujube. I've got two of these rather large, productive jujube trees, and while all my other trees are generally under siege by raccoons, possums, squirrels, rats, and red-bellied woodpeckers, nothing ever touches my jujubes.
Why this is so, I have no idea. I'm just grateful.