Unless your TL includes a major change in the attitude of the US government, I don't think the US would accept a large number of South African refugees. Johnson's immigration reform bill was specifically designed to move away from racially focused quotas and emphasize immigration of people with specialized skills or relatives already in the U.S. Most white South Africans wouldn't qualify on either count.
True, but what about the Cold War angle? I don't think most of the Southeast Asian refugees who settled here in the '70s had specialized skills, and I know that almost none of them had relatives in the US. If the South Africans are fleeing a new communist regime, some allowances may be made as they were for Vietnamese, Hmong, Cambodian, etc. immigrants.