I think that white does symbolize purity in the novel, but not in the traditional sense. Culturally, the West often associates white with innocence and chastity, which is sometimes called sexual purity. However, Fitzgerald uses white in his descriptions of the Old Money class within the novel, those characters being Daisy and Jordan. This suggests that white represents class purity; the only people who wear white and have white houses with white curtains in them are members of the wealthy elite.
While Gatsby certainly tries to emulate the elite, he is not considered to be purely one of them because of his low-class background and shady business dealings. Notice that in descriptions of his clothes and possessions, the colors are often bright and varied—in other words, not white.
Furthermore, in the apartment party from chapter 2, Myrtle Wilson changes into a dress of billowy “cream-colored chiffon.” While cream is a shade of white, it is not a pure white. This suggests that Myrtle wants to think of herself as pure class via her affair with a bona fide elite (Tom), but her working class status can’t ever be removed. She might be able to get close to “pure” white, but she will never actually be one of the wealthy elite.
Another way you could look at whiteness as a representation of purity is Tom’s tirade about the “Rise of the Colored Empires” in the beginning of the novel. Tom is infuriated at what he sees as the slipping position of the white man’s place in the world. If white actually represents the upper class in the text, then Tom could actually be expressing his anxiety about the New Money types who he thinks are encroaching on his territory of social status. This could explain why he judges Gatsby from the beginning, and perhaps why he doesn’t see him as a romantic rival until later in the text.