As a side question to branch of this one - how common was segregation in illegal activities in general before the civil rights movement? (The one that comes to mind specifically is illegal alcohol manufacture/sale, but there are a wide array of organized criminal activities in America.)

You might be interested in the district of Storyville in New Orleans, where prostitution was legalized from the late 19th century to the First World War.

To answer your question, prostitutes were indeed segregated and categorized by race in Storyville. In fact, the brothels published a "Blue Book" that contained photos and descriptions of popular women, annotated with symbols (“w” for white, “c” for colored, “J” for Jewish and “oct.” for octoroon).

But the best bordellos banned black men, so interracial sex tended to go in one direction.

For more detail, see Emily Epstein Landau, Spectacular Wickedness: Sex, Race, and Memory in Storyville, New Orleans

On the evolution of red-light districts in the US (with some mention of race), see this lecture by Melissa Gira Grant.

You may want to come back on the 29th. We'll have Jessica Pliley doing an AMA. She's written a history of the Mann Act, which specifically targeted prostitution.