ATL During both World Wars, English-born immigrants rushed to the sound of guns, ergo, they suffered far heavier casualties than Bakers. These heavy casualties gutted the British upper class in both Rhodesia and South Africa. By the end of WW2, Boers were numerous enough to dominate politics in Rhodesia and South Africa.
Meanwhile, Britain was exhausted by the wars and could no longer afford to police far-flung colonies.
Britain was further weakened by the Bretton Woods Agreements which allowed free trade in her colonies. Free trade eliminated trade imbalances favourable to Britain. Free trade also allowed the intact American economy to expand into British colonies.
The end result was that local Boers re-gain control of Rhodesia and South Africa

ATL Fewer major wars mean fewer British-born casualties and the English-speaking upper crust retains power in Rhodesia and South Africa. Apartheid never becomes official or as harsh. Brits slowly educate the brightest blacks and slowly allow them into lower-level management.
 
Probably less migration from UK. Pre Ww2, the white population was about 75k (mainly Anglo, but with lots of Afrikaner and, oddly, Jewish peoples). Post war, along with everywhere else, Rhodesia received vast numbers of migrants from UK, for all the usual reasons.

Wikipedia says for one about quarter of a million whites migrated into Rhodesia 54-72 (about the same apparently emigrated too).
 
And how would the lack of the world wars change the results of a referendum?

A great many Rhodesians believed that many Boers had shown themselves to be disloyal to Great Britain during the First World War and didn't want to be part of the same state as them.

"Meanwhile the outbreak of the World War for a time forced the constitutional question into the background. But the war itself had an important bearing on the political question. The party which desired the indefinite continuance of Chartered Co. rule had nearly disappeared, but an influential party had advocated, as the alternative to self-government, joining the Union of South Africa. This party lost ground as Rhodesians saw what was happening in the Union. The growth of separatist and republican sentiment among the Dutch population, evidenced by the increasing support gained by Gen. Hertzog and particularly the rebellion of 1914, inevitably influenced the political orientation of the almost solid British population of Rhodesia. Disinclination to be swallowed up in the Union and dislike of the introduction of bi-lingualism—a necessary result of Rhodesia becoming a province of the Union—were strongly reinforced by real if perhaps exaggerated fears as to the strength of the Dutch nationalist movement..." https://en.wikisource.org/wiki/1922_Encyclopædia_Britannica/Rhodesia
 
Top