What about the "hypothetical person" on an island who has never heard about Jesus or has no idea about the Bible, etc...And he's a full grown male. How can he accept this?
Ah, the "man on the island."
Every living being is consciously aware that there is a higher power - "The heavens declare God’s glory, the skies proclaim the work of His hands” (Psalm 19:1). This is pretty much the same about people who are mentally handicapped. Whether they know the story (Jesus coming to earth, etc) or not, they will be judged accordingly to their knowledge.
Luke 12:48 - "To whom much is given much is required." Mentally handicapped/the man on the island only are only given so much knowledge and I think God will judge them according to their knowledge.