Oh, this is definitely a hard choice. It's a debate between "The Five People You Meet In Heaven", "Tales of The Bounty Hunters", and I'm sure I'm forgetting a few other books hat I unfortunately can't think of.
Perhaps that is their preference? How is them choosing the bible not illustrating their preference or perhaps the book they hold to be most important and not want to part with if they could help it? Besides not everyone said the bible or quran anyway which clearly disproves your point that allowing it would lead to only those answers as others have listed other books besides those two holy books.
I would pick the bible myself as all those other books won't keep your interest forever as soon they will get put aside and forgotten on that island nor will they inspire you to have hope during trying times on such an island if you are a believer of course.
Any thing by Michael W. Smith. My top two choices would be "It's Time to be Bold" and "This Is Your Time". Or maybe I'd grab both. I guess it depends on how long one would be staying on the island, really.