So, I just want to make this clear off the bat, I am not a rhodie fanboy, and fully realize how racist their regime was, but that being said, how come despite having a similar government, the U.S, while formally denouncing them as well, decided clandestinely to keep relations going with Apartheid South Africa through such policies like the Tar Baby Option and providing logistical/intelligence support during the Angolan Border War, but never assisted, and were in fact instrumental in the demise of Rhodesia (when Kissinger forced South Africa to break ties with them, leaving them without a trading partner and unable to keep their economy going) despite the fact they were also fighting a communist insurgency, and by going against them they were advertently allowing communism to spread on the continent.
The most likely reason was because it was easier to toss aside Rhodesia, being a smaller economy, especially because the main products of Rhodesia were copper and other minerals, The US had already secured a market for that from Zaire.
As well South Africa was a nuclear state as early as 1967 so the value that South Africa presented was far greater both as an economic and a military partner.
For the most part, the powers picked and chose when to get involved in Africa. They allowed socialism in places like Tanzania, Guinea, and Ghana, but were resistant to even inklings of it in Egypt, Angola, Mozambique, and South Africa.
At the end of the day it comes down to strategic value. The Congo and South Africa provided more value than Rhodesia ever could, so the US made the decision to cut them out.