In mid-20th century America, the turban was a tool that people of color used for "confounding the color lines," writes Manan Desai, board member of the South Asian American Digital Archive.
At the time, ideas of race in America were quite literally black and white. In some places, if you could pass yourself off as something other than black, you could circumvent some amount of discrimination. People of color — both foreigners and African-Americans — employed this to their advantage. Some did it just to get by in a racist society, some to make a political statement, and others — performers and businessmen — to gain access to fame and money they wouldn't have otherwise had.