In Buried in Bitter Water by Elliot Jaspin, he mentions that in Gainesville, Forsyth County, the farmers' market was one of very few desegregated spaces. The daughter of Mae Crow, Esta, recalls a close friend, Lillian Koch, who made her money from retail:
"I had been told Lillian was Jewish but I had also been told not to tell anybody that she was Jewish," Debbie Said. "If people had known she was a Jew, people wouldn't have done business with her."
Hence the question.
There certainly was antisemitism in the southern US, both before and after the civil rights movement (which really had very little to do with antisemitism at all). Perhaps the most infamous example of this is the lynching of Leo Frank, a Jewish factory manager and a fairly prominent member of the Jewish community in Atlanta. He was convicted of murdering a girl who worked at his pencil factory, but there was very little evidence against him. His sentence was commuted from death to life imprisonment, but he was lynched soon after.
But the important thing is that Jews were considered firmly on the white side of the black/white racial divide of the south. Yes, they were not a sort of white that was looked on favorably, and they were subject to discrimination and hatred. But they were solidly on the white side of the racial hierarchy, albeit on the less privileged end of it. This meant that Jews were not subject to nearly the same social or legal disabilities that black people were.