What is the central theme in the novel? How is the theme conveyed through characters, the setting, symbolism, and so on? What are examples of this theme as it appears throughout the novel? Explain why you chose this as the central theme.

There are many themes we could choose to discuss in Geraldine Brooks's novel Caleb's Crossing (2011). These include the significance of names, the contrast between country life and city life, and the cycle of life and death.
However, one theme that I think would be particularly interesting to highlight is the importance of individual identity. What makes us who we are? How do the characters find their identities, and how do they struggle in the process? Let us talk about this with respect to the novel's various elements you mentioned in your question: characters, setting, and symbols.
CHARACTERS
Bethia is the novel's protagonist. The story opens when she is 15. Her name means "servant," and she struggles with it: she is a young modern woman. She lives in a conservative place (in a Puritan settlement on Martha’s Vineyard). She studies in secret, even though she is not supposed to. Additionally, she wants to be treated with the same fairness and respect as her brother, but she knows that the society she lives in considers him her superior. She does not want to be a "servant," although her name, given at birth, designates that role for her. She is somewhat at odds with her identity as a female. Additionally, she has more interest in the spirituality of the island's indigenous group than in the religion she is being raised in.

I had come to think that the Wampanoag, who dealt so kindly with their babes, were wiser than we in this. What profit was there in requiring little ones to behave like adults? Why bridle their spirits and struggle to break their God-given nature before they had the least understanding of what was wanted of them?

This brings us to the next point.
Caleb, the book's other main character, also struggles with his identity. He is part of the island's indigenous tribe, the Wampanoag. Early in the book, he becomes friends with Bethia. He is interested in the book she is reading.

I held it out and Caleb took it. This was the first book he had held in his hands. He made me smile, opening it upside down and back to front, but he touched the pages with the utmost care, as if gentling some fragile-boned wild thing. The godliest among us did not touch the Bible with such reverence as he showed to that small book.

When he asks her for it, she says it is not hers to give. Caleb has no grasp of the idea of personal property—he was raised in another culture, with the Wampanoag—and he is hurt. He does not fit in with Bethia's world any more than she fits in with his. However, they are both curious about the worlds outside their own communities, and they both struggle to define themselves in that larger context.
SETTING
The setting of the book involves two specific settings that rarely overlap despite the fact that they are right next to each other. Bethia's Puritan community and Caleb's community, where the Wampanoag live, both constrain identity to a certain set of social norms, traditions, and behaviors. As mentioned above, it is difficult for a person from one of these settings to find (or feel comfortable in) his identity in the other.
SYMBOLS
Books are important symbols in Caleb's Crossing. As we saw in the passage quoted above, Bethia's father's book is a symbol of his identity, and the identity he wants for his daughter. Caleb wants the book because he is drawn to what it means and what it contains.
Books also represent escape from one's identity, especially as it pertains to social roles. As Bethia observes, her father uses his books to avoid intimacy with his wife:

My mother was an excellent woman. Pious, virtuous. Kind. But she was not the intellectual equal of my father. Not by any means. I do not speak of book learning. I speak of a certain innate quality of mind, a superior understanding. Because she had it not, their companionship was—diminished. Father looked to his books, rather than to his wife.

Books, whether between Bethia and Caleb or between Bethia's parents, symbolize the gap between two identities.