The theme is best represented by Phillip's blindness. Phillip is a young boy who has been conditioned to believe that colored people are somehow beneath them because of their color and in his defense, much of the world, at the time, believed this as well, including Timothy. Timothy demonstrates "knowing his place" by always calling Phillip "young bahss" or "young boss".

Soon after the shipwreck and Phillip's head injury he becomes totally blind. After several months on the Cay Timothy teaches Phillip how to survive and be independent because he knows that his own death is near. Little by little Phillip begins to see Timothy as a friend and a mentor rather than a slave or a lesser being.

Phillip actually does not even see Timothy as "colored" any longer. He loses his feelings of prejudice and superiority as a result of being lost on this island.

Some other themes might be self reliance, friendship overcoming adversity, and grieving losses.

Actually, upon a little further research, I am more inclined to lean towards the themes of racism and prejudice as the main themes of The Cay.  I believe that Taylor’s intention was to demonstrate the elimination of prejudices based on the model friendship shared by Phillip and Timothy. Check out the link below to read more on this particular theme.

What is the theme of The Cay by Theodore Taylor?

In The Cay, 11-year-old Phillip is traveling on a boat that is attacked by German submarines. As a result of the attack, Phillip is blinded and ends up on a lifeboat with Timothy, another survivor of the shipwreck. The two eventually was up on an island and have to work together to survive, awaiting an eventual rescue.

The theme of this story is one of survival, friendship, and trust, particularly between people of radically different backgrounds. Phillip is a child from Virginia with a good family. Timothy, on the other hand, is an old man who has spent his entire life working on ships. As a child, he was an orphan who never learned his exact age or attended school. Despite these differences, the two become closer than seemingly possible while trying to survive on the island.

What is the theme of "The Cay"?  

The primary theme of Theodore Taylor's novel, The Cay, is that of racial prejudice. The main character, young Phillip Enright, maintains a distrust of the black natives of Curacao, in part because of his mother's Southern (Virginia) upbringing. Through his own blindness, Phillip comes to see the innate goodness of the old St. Thomian sailor, Timothy. In the end, Timothy saves Phillip's life not only from drowning and the sharks but also from the hurricane, and the boy becomes forever indebted.

Anti-war sentiment also seems to be a secondary theme in the novel. Taylors shows how the horrors of war disrupts the otherwise peaceful tranquility of the seemingly remote island of Curacao.

What is the theme of The Cay?

Clearly one of the central themes of this great classic is racial discrimination and how it is overcome. The fact that Philip is stranded on an island with just Timothy to look after and help him forces him to confront his own racist notions that he has received from his parents, in particular his mother, and he emerges from his experience a changed individual who no longer judges someone's character based on the colour of their skin. Note how Philip is presented when he realises his superiority to Timothy:

I felt good. I knew how to do something that Timothy couldn't do. He couldn't spell. I felt superior to Timothy that day, but I let him play his little game, pretending not to know that he really couldn't spell.

However, it is clear that his attitude changes, as we can observe when Timothy is buried by Philip. Of course, being blind means that Philip has been completely dependent on Timothy, which has forced him to re-learn a number of different things, not least how to survive with his new limitations, but also how to value other humans. Let us consider this change in action:

I buried Timothy, placing stones at the head of the grave to mark it. I didn't know what to say over the grave. I said, "Thank you, Timothy," and then turned my face to the sky. I said, "Take care of him, God, he was good to me."

The message of the novel seems to be clear. Philip has been forced to confront and conquer his own racism and sense of superiority, admitting his dependence on Timothy and how Timothy has been the one to look after him but also the one to teach him how to survive. He emerges from the experience a different, and more enlightened, individual.