The issue was not that they would not be accepted but how the western world be able to handle that many refugees in a short period of time. How that would impact countries like Canada, Australia, New Zealand. Even UK and USA would struggle to process and assimilate that many people.
And the domestic political implications would be very interesting. The white refugees would be AT LEAST as anti-Communist as the Vietnamese Boat People, with a not-so-subtle overlay of white-supremacy. They're probably not gonna be voting for anyone to the left of Jesse Helms.
(For the record, I know white South Africans, and they're not generally like what I describe above. But, of course, we're talking about a time-line where they're fleeing Communism.)