Friendship
The film is primarily focused on the friendship between two men who are unlikely to form a bond. When the effete Don Shirley hires the rougher Tony Vallelonga to be his bodyguard, he is looking for someone with brawn and an intimidation factor to keep him safe in the prejudiced American South. Both of the men are skeptical of one another; Tony thinks Don could stand to loosen up, and Don finds Tony coarse and unrefined. As the film progresses, however, these differences, and the ways the men try to bridge the gap between these them, become the substance of their friendship, allowing them to find commonality and mutual admiration. The film is primarily concerned with depicting the ways that friendships form and endure, the ways that people who do not have much in common can find common ground.
Race
The film is also very much about race, as it tracks a white, initially bigoted Italian-American man driving a black man through the South on a concert tour. The title takes its name from a popular guidebook of the time that listed all of the hotels and restaurants in the South that were friendly to black people. The South, in the early 1960s, was segregated on racial lines, and was not always welcoming to black patrons, even someone as renowned and well-respected as Don Shirley. The film examines the history of racial prejudice in America, showing the ways that institutions and people can think they are progressive when they are in fact holding onto racist and bigoted beliefs. It also seeks to challenge different preconceptions and stereotypes about race; for instance, Tony is surprised to hear that Don does not know popular black music of the era, nor has he ever had fried chicken, a stereotypically black food item. Through the lens of the driver and his boss' friendship, the audience sees many perspectives on the subject of race, and the film seeks to depict the American quest for racial equality.
Segregation
More specifically, the film examines segregation in the South. In the North, there are no explicit barriers preventing black people from entering white establishments, even if there are unspoken boundaries. In the South, however, the boundaries are explicit and exclusionary. The purpose of the Green Book is to help people find hotels and restaurants that are amenable to black patrons, and on more than one occasion, Don is welcome to play at a venue, but not afforded other luxuries of being a guest. At one venue, the host tells Don to use an outhouse rather than an indoor restroom, and in Birmingham, Don is not allowed to eat in a restaurant at which he has been contracted to play. Segregation is an explicit manifestation of racial prejudice and white supremacy, a way to marginalize and disrespect black people in the American South.
Rough vs. Refined
The differences between Tony and Don are central to the thematic fabric of the film. Where Don is refined, cultured, and polite, sometimes to the point of fussiness, Tony is crass, rough-around-the-edges, and forthcoming, snarling at anyone who looks at him funny and chewing with his mouth open. The two men could not be more different, a kind of Goofus and Gallant pairing whose contrasts often strike a comic tone.
Music
Don Shirley is, after all, a musician, the best of the best. The calling card that grants Don access to such predominately white spaces is his musical talent, which, as he tells Tony, makes his listeners "feel cultured," even though they do not see him as an equal. Don is a "virtuoso," a musical prodigy from a young age who has made his life about his music. A master of many genres, Don tells Tony that he prefers playing classical music above anything else, but that he is discouraged from doing so because of his race, so has started playing popular music to appease his record company. Music is a huge part of the film, from scenes of Don playing at different venues throughout the country, to Tony introducing Don to Little Richard and Aretha Franklin when they are playing on the car radio.
Love
Another theme in the film is love, both platonic and romantic. By the end of their trip, Tony and Don share a deep admiration and love for one another, based on their mutual understanding and appreciation for what the other has taught them. Tony, who was once afraid to have black repairmen in his home, welcomes Don to Christmas dinner as his dear friend. Don, isolated by his career and his meticulous work ethic, chooses love by attending the dinner on Christmas Eve and opening up.
Additionally, the romantic love between Dolores and Tony is important to the film. They are in love, but when Tony is forced to take the job as a driver, they must face two months away from each other. Dolores tells him to write her letters, which he does obediently, but they are not very good. Don helps Tony spruce up his writing, weaving poetic, expressive, and romantic notes that capture her heart. When he returns on Christmas Eve, she has fallen even more deeply in love with him, enamored with his ability to express his feelings for her.
Sexuality
While it is barely touched upon, sexuality is another one of the film's themes. Don is found at the YMCA, arrested after getting into some kind of altercation in the showers. It is implied that the manager found Don in a sexual situation with a white man, and after Tony pays off the cops, he warns Don that if word got out about the scandal, it could ruin his career. The script does not say it outright, but it is implied that Don engages in same-sex relations, yet another element of his identity that isolates him from the world. Later, he tearfully asks Tony, "...if I’m not black enough, and if I’m not white enough, and if I’m not man enough, then tell me Tony, what am I?!" In this, his suggestion that he is "not man enough" is likely a nod to his homosexual proclivities, yet another facet of his identity that makes him feel outside or other.