Genuine question: how much does that matter, or how much could it matter in the future?
I know the ANC is experiencing rapid political degeneration, but as far as I know (looking at it from Europe) the movement as a whole is still as diverse in its membership as South Africa is as a whole.
There have been some rumblings about it, and in the last election the only province where the ANC increased its support was in KwaZulu-Natal, the only province with a Zulu majority. This was probably because Zuma is a Zulu.
There are few ethnically-based parties in South Africa. There is only really the Zulu Inkatha Freedom Party (which has a surprisingly diverse leadership, three of its prominent members of parliament are an ethnic Indian, a white Afrikaner, and an Italian immigrant) and the Freedom Front Plus, which is an explicitly white Afrikaner party.
The ANC's leadership is still quite diverse and still has quite a few whites within its leadership.
I don't think tribalism will become a major problem in the near future, but who can say what the situation will be in the next decade or two.