Simply put, South Africa had legally been granted progressive self-governance and independence through dominion status in the British Empire, which by 1934 effectively meant complete independence. From an international legal perspective, it was sovereign. That isn't to say that plenty of critics treated it as one, given that it was a state that until 1994 lacked any semblance of majority rule and couldn't claim to have the consent of the governed.

Now, of course, plenty of states had either fraught relations with South Africa, or none at all. Some of the Scandinavian states took the step of just directly funding the liberation movements, as did the Eastern Bloc states, and most of the rest of the African states tended to act as though the government of South Africa was illegitimate.

Rhodesia is a different matter because it was legally considered a colony at the time of the UDI in 1965. Britain had established that there would be no independence for its colonies that had not undergone a transition to majority rule. Great Britain immediately deemed the UDI illegal, as did the United Nations, and any support for recognizing Rhodesia was open to criticism that it was both illegal and explicitly in support of white supremacy.