Southern Italians in particular were not considered by all and sundry to be "white" until some time after WW2. The book "An offer we can't refuse" by George DeStefano goes into the perceptions in some detail.

There was a famous case in 1922 Alabama where a black man was convicted of having consensual sex with a white woman but a higher court threw out the conviction because it was not convinced that the woman, of Sicilian ancestry, was white. Similarly people like Louis Prima occasionally had trouble getting work in some NY clubs because people wanted to make sure he wasn't a black man trying to pass. And of course in 1925 the Irish gangster Peg Leg Lonergan, the night he was killed, chased off three Irish women with Italian dates, telling them to "come back with white men".