Boo Radley is not only white, but he is as white as a ghost. He has not seen the light of day since he was a young boy. After he "stabbed" his parents with the scissors, he was first detained in the county courthouse prison and then in his own house for years.
TKAM was set in the deep South, where Jim Crow laws kept blacks from integrating with whites in schools and neighborhoods. In other words, the whites live in white neighborhoods and the black live in black ones. The Radleys live across the street from the Finches in the white section of Maycomb. The Robinsons would have lived outside the city center in a black neighborhood. There, they would attend an all-black church, the First Purchase church. Cal invites the kids there; white adults would not have been so open minded in attendance.
Remember when Boo's brother shoots at the kids when they were snooping? Pressed for a description of the suspect, Nathan Radley says it was a black man who must have been trying to rob him--such was the racism and fear of integration in the all-white neighborhood.
Although I do not think it is ever definitely stated, it is clear to me that they are definitely white.
For example, in the first chapter, it talks about how Boo joined the nearest thing that Maycomb had to a gang. He and his friends go around causing trouble. They eventually get charged with using bad language near a lady. But before that, no one had the nerve to tell Mr. Radley that Boo was hanging out with a bad crowd. In that society, there is no way that white people would ever have thought twice about telling a black man what was wrong with his son. And it is likely that the police would have come down hard on their "gang" if they had been black. After all, think about what happens to Tom Robinson, who is black.
I think they are white because after Boo Radley was involved in the "gang" he was about to be sent to some sort of prison but the sheriff didnt want to place him in a prison alongside with the "negroes"