I don't think China would be necessarily an open ally of such a regime, but rather indifferent to such a regime and openly trade with it. In return, China would openly trade with such a regime and probably become its largest trading partner. I imagine that official diplomatic relations might not even be a hindrance, and any such regime might continue to have formal relations with Taiwan.
After Nixon's trip to China, the world view of the People's Republic changed. This was especially true after 1979 when China began to view its relations with the world in an almost exclusively economic fashion. This pragmatism has led to China investing in and openly trading with some of the most brutal regimes on earth. It also led to less aid to Communist guerrilla movements and their allies. When Western nations impose sanctions on countries (Myanmar, Sudan), China usually is more than happy to fill the vacuum. Additionally, after Tienanmen in 1989, China's foreign policy adheres to Westphalian Sovereignty, meaning that it should not interfere in the internal policies of sovereign nations. Despite ideological differences, this doctrine was one defended by South Africa and Rhodesia.
China's Five Principles of Peaceful Coexistence, originally formulated for relations with India, can actually be summarized as a guide for China's relations with all nations. Whereas the West's attachment to democracy and human rights has undermined the principle of Westphalian Sovereignty.
China's Five Principles of Peaceful Coexistence
1. Mutual respect for each other's territorial integrity and sovereignty.
2. Mutual non-aggression.
3. Mutual non-interference in each other's internal affairs.
4. Equality and cooperation for mutual benefit.
5. Peaceful co-existence.
Prior to 1989, China's trade with South Africa was small but steadily increasing, so any South African or Rhodesian regime would probably enjoy the benefits of increasing Chinese trade. Japan, Taiwan and South Korea too were interesting insofar as Japan had become South Africa's leading trading and investment partner after 1985. Like China of today, it was mostly concerned with returns on investment, and South Africa presented an opportunity for Toyota and other firms. Despite this, Japan maintained low-level official diplomatic links. Taiwan, a country with fewer official diplomatic links and no longer a member of UN was only too happy to maintain relations with South Africa and even allow South African Airways to begin flights to Taipei in 1983. South Korea had no official relations, but its firms were increasingly investing in SA by the late 1980s, and I imagine with the growth experienced by South Korean firms like Samsung, LG etc since the 1990s, they too would not be adverse to selling their wares in South Africa or Rhodesia.
Putin's Russia would be interesting as well. Around 1989, the first relations with the Soviet Union and South Africa were being forged and the country was trying to attempt to recruit immigrants in Russia, even airing ads in the country. With the bogey of Communism gone, there were those in South Africa who saw an opportunity to boost the white population by attracting Eastern Europeans, particularly those with skills in engineering and especially in the military-industrial complex. Considering that the ex-Soviet economies continued to plummet in GDP until around 1999/2000, South Africa could still be attractive enough of a place for these immigrants. Additionally, as military hardware was one of the few sources of export income during the 1990s, one can envision a scenario where some of it ends up in SA. What I can see happening is a large enough Russian community in the country emerging (250,000) and Putin using this as an excuse to want to safeguard their interests. Meaning Russia would not be openly allied to South Africa, but probably bloc sanctions in the UN, on the premise that the US and Europe and trying to expand their influence and interfere in the internal affairs of a sovereign nation.