Is it possible? What would the ramifications be?
I'd imagine this would be in a context where the conservative politicians in the US and UK are openly supporting and recognizing the Apartheid regimes, perhaps due to more diligent (or zealous) anti-communist ideology. That is to say, they openly support Rhodesia against the ZANU and ZAPU simply because of the support of the Chinese and Soviet Union respectively. To allow this to happen, the electorate of the US and UK would probably have to be more willing to support international anti-communist activity.
If you want to get into ASB territory, a diplomatic split between the US and UK on recognizing Rhodesia (the former recognizing and supporting Rhodesia after UDI), perhaps.