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.

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.

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.

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.

I love that this book deals with disabilities and that people with disabilities like blindness or amputations aren't different mentally, emotionally, or spiritually than able-bodied people.  My father was disabled and people always spoke more loudly to him even though his ears worked just fine--he was a double amputee (both legs below the knees).  I never knew we weren't "normal."

One thing that The Cay teaches us is that prejudices are illogical. If Timothy did not have a distinctive dialect, Philip might never have known that he was a different color. Also, if Philip's mother had not taught him to feel superior to people of color, Philip and Timothy might have had a better relationship from the start.

Another lesson the book teaches us is that having a disability doesn't necessarily mean that we are not able take care of ourselves. Although he is blind, Philip is able to find food and shelter for himself after Timothy dies. He doesn't let blindness hold him back.

Despite being a brief novel, TheCay includes many important ideas throughout the text. One such idea or theme is focused on racism. Phillip is an incredibly racist child at the beginning of the book, and he speaks quite abusively to Timothy on multiple occasions. To be fair, Phillip also cruelly talks to his own mother; however, Phillip's insults against Timothy come from his belief that black people are inferior. Phillip will learn that his beliefs are wrong, and he will come to love and appreciate Timothy. The two characters develop an incredibly strong bond while on the island, and it is heartbreaking when Timothy dies.

The book also includes powerful messages about perseverance. Timothy and Phillip are in a tough situation. The small cay that they are on is not overflowing with water sources or food sources. They have to work hard to survive, and Phillip has to learn to do it all without the use of his sight. He initially feels that he can't do anything while being blind, but he learns through hard work and dedication enough skills to survive on the island without Timothy's help.

Finally, the book teaches readers that having hope is important. Timothy knows that they are not on an island near a busy shipping lane. He knows their chances of rescue are slim, yet he never allows himself or Phillip to wallow in self pity. Hope is something that both characters cling to because it is a motivator to keep on surviving.

Theodore Taylor's novel, The Cay, touches on several themes, including those of friendship and racism as you mentioned in your question. Phillip learns to overcome his own racist outlook through the friendship he develops with Timothy, the West Indian sailor who saves his life on several occasions. Phillip has inherited his racist outlook from his mother, a native of Virginia. However, through Timothy's good deeds, loving companionship and fatherly advice, Phillip--though blind--comes to see that color does not always matter. Timothy, too, is able to look past the young boy's condescending manner, realizing that his immaturity is the impetus behind his feelings. In the end, Phillip comes to love Timothy, and when he returns to his home, he finds that he wants to spend more time with the local native populace in the hope of better understanding them--and perhaps to meet some of Timothy's old acquaintances. The novel also gives a glimpse into West Indian life during World War II, a subject neglected in modern literature.