Racism
One of the main themes of Noughts & Crosses is racism. Crosses, with dark skin, are seen as the superior race, and noughts are understood to be inferior. The world of the novel has many close parallels to the era of the civil rights movement and the Jim Crow era in America in the 20th century. The theme of racism is explored in large racist gestures—racial violence including Lynette being beaten and a Cross shopping center being bombed—as well as the microaggressions faced by noughts, such as Band-Aids being made for black skin instead of white, increased suspicion in public spaces, and frequent identity checks and police harassment.
Religion
Noughts & Crosses explores the theme of religion and who religion is for. Crosses are believed to be higher in society because they are closer to God than noughts. The religious holiday in the winter is called Crossmas. The theme of religion is more complex for noughts, as Callum says that no noughts believe in God, but then he discovers his parents—particularly Ryan—praying to God. As Callum is about to be hanged, he decides not to pray, since he didn't really believe in God when he was alive; however, as he walks out of his cell, he begins to pray, and he dies thanking God that he can hear Sephy's voice.
Friendship
Though Noughts & Crosses depicts racism and hatred, in many ways it is a story about the theme of friendship. Callum and Sephy are forbidden from being friends, but they persevere, and their connection blossoms into love. Sephy's other peers, whom she considers her friends, turn against her when she tries to sit at Callum's lunch table. Mrs. Hadley tries to be friends with the McGregors across racial barriers, but she's not willing to go against society—she might secretly pay Ryan's legal fees, but Sephy decides that this isn't enough action for real friendship. The novel seems to conclude that friendship is an active, present force, not simply grand gestures for people you love.
Love
One of the primary themes of Noughts & Crosses is love, as Callum and Sephy continually choose each other against all odds. Their star-crossed love drives the plot of the novel, but there are other forms of love explored in the novel too, as well as failed love. Meggie and Ryan love their family, and they each take the action they think is right to protect them, with Meggie kicking Ryan out and Ryan becoming an active member of the L.M. The Hadley family shows a similarly complex take on love, with Sephy's parents separated and often fighting; Jasmine's love for Sephy and Minerva is crushing and selfish, and it pushes Sephy to go away to boarding school so she can become her own person.
Language
Noughts & Crosses explores a theme of language: how the words we use determine how we think, feel, and act, in both difficult situations and day-to-day life. There are small examples of this (for example, Callum observes that for Kelani Adams, "obviously the phrase 'a lost cause' wasn't part of her vocabulary," explaining why she's not willing to give up Ryan's criminal case) as well as large ones. Jude's use of extreme language, like calling Crosses "daggers," transitions into his use of extreme violence against those Crosses. When Sephy uses the word "blankers," Callum makes her promise never to say it again, forcing her to consider the language she uses and the effects it has on other people as well as her own thought processes.
Responsibility
Another theme of the novel is responsibility, reflected in the characters' frequent return to the idea of "making a difference." Callum feels left out and hopeless—he loses his sense of responsibility for his actions, relying on hatred instead. Sephy grows from feeling like her one voice can't change anything about society, to participating in protests and sit-ins, and eventually to telling everyone loudly and proudly that Callum didn't rape her and that she loves him. Noughts & Crosses asks which, if any, of our choices are our own (with frequent declarations like "it's all her fault"; "he's making me feel guilty"; "if only he weren't a nought"; etc), and which are brought on by our society at large. It also asks us to interrogate what we can change about our society to make our world a better place, encouraging us to ponder whether violence is an appropriate answer to hatred and inequality, and whether radical action has a place as a form of protest.
Hate
Noughts & Crosses explores the theme of hate. Who hates who, and why, are central to the novel. The most obvious version of this is racial hatred, which Sephy and Callum sometimes feel themselves, and sometimes are highly critical of. The novel also depicts interpersonal hatred, particularly in families: Kamal hates Jasmine, bearing resentments from before Sephy was even born; Meggie comes to hate Ryan for joining the L.M. and putting her sons in danger, though that hate is tied very closely to her love for him.
All of these themes combine into a complicated central plot point, which is how hatred develops into terrorism. Callum doesn't join the L.M. and kill Crosses simply because he hates them; all of these themes combined—from love to responsibility to language to hatred—help the novel explore the forces that convert a sensitive, intelligent young person into someone who commits race-based violence.