Lets get some context first of all. Zim and SA are totally diferent cases. In Zim prior to 2000 the minorities refused to participate in politics. There may be a reason for this, I'm not totally clued up on Zim's history.
But I can just imagine that a scenario in Zim where very few white people participated in public life must've have bred some resentment with the majority of the population- especially those who war veterans who were landless and whose struggle seemed to be in vain. While white farmers were (seemed to be) living off the fat of the land.
In South Africa minorities actively participate in public life and you don't get the image of the rich white farmer living it up while the rest of the population struggles. Granted, we have a way to go when it comes to reducing the income gap but South Africa is nowhere near where Zim was in the early 90s and some of the economic upheavals that turned Uncle Bob into a hater of all things Western when he had built his image on being a civilised native. Although their historical paths seems similar, comparing the two is nonsense.
Maybe I'm missing something but why would white people not voting breed resentment? In SA most white people don't vote ANC so surely the ANC and their supporters would rather they didn't vote?