Segregation takes place in at least two ways in the novel. Class and race are the basis for distinctions of value and character and even of justice. Segregation occurs in public but is reinforced in private, as in the conversation held by the society ladies invited to the Finch house by Alexandra.
The theme of coming of age is really how the author presents the other themes and ideas in the book. We are willing to accept Scout's opinions and ideas because she is an innocent child. As the novel progresses, Scout begins to loose some of this innocence. Her eyes are opened to discrimination and the injustice of the world around her. She see the injustice and discrimination of both Tom and Boo Radley. We accept her views on things with less prejudice because she is an innocent child.
Coming of age relates to the other two themes. As Scout gets older, she learns the truths of her society. These are things adults take for granted, like prejudice. As the novel progresses, Scout learns more about life and realizes that not all people accept racial injustice.
As for segregation, it was the way of the American South (and much of the North) during the 1930s and well beyond. It may seem unusual now, but separate schools, restaurants, restrooms, churches, hotels and neigbhorhoods for blacks and whites were the norm at the time of the story.
Social injustice was alive in TKAM just as it is in many ways today. African-Americans were considered inferior by many white people; Boo's mental state relegated him to an outcast; the Cunninghams are outsiders because of their poor financial situation and their distant homes in Old Sarum; and no one will have anything to do with the Ewells because of their past (and present) reputation.
The three children--Jem, Scout and Dill--experience a coming of age during the first half of the novel, primarily through their contact (though minimal) with Boo. They learn that Atticus has a secret or two up his sleeve, and Jem discovers a new meaning of courage. Their loss of innocence only grows in Part Two.