The narrator's musical ambitions are connected very strongly to his "blackness"; he wants to find a way to merge ragtime -- an African-American musical form-- with European classical music.
The problem is that he is tempted to take advantage of his light skin color and try to "pass" as a white man. This would have been a temptation to any African-American of light skin color in those times of open racism.
The narrator makes his decision after he witnesses the lynching of a black man (see link below). Instead of causing him to hate whites, this incident produces in him a terrible shame and embarrassment about being black; he becomes ashamed of "being identified with a people that could with impunity be treated worse than animals."
He begins to pass himself off as a white businessman, and soon becomes quite successful. His fate is sealed when he meets and falls in love with a beautiful white woman. Although he eventually admits to her his origins, he cannot marry her, and live with her the life that he wishes to, if he reveals his origins to anyone else.
The Autobiography of an Ex-Coloured Man by James Weldon Johnson is the story of a nameless protagonist of mixed racial heritage. He is the son of a wealthy southern gentleman and a black woman. While his father is distant and only visits twice, the father does send sufficient money to help the narrator live in a wealthy white neighborhood and get a good education. The narrator is also light skinned and thus able to "pass" as white.
The narrator had been torn between loyalty to his two races, at first wanting to express his dual heritage by fusing ragtime with classical music but also aware of the degree to which black people were mistreated. The key moment in his decision to pass as white and become a successful businessman instead of devoting himself to his musical vision was witnessing a lynching in Georgia. He is horrified by the violence and the inaction of the spectators and in response decides to renounce his black heritage (including his music) and "pass" as a white man.