For three decades, power in South Africa has had a three-letter name: The ANC, or the African National Congress. The political party once led by Nelson Mandela has been a powerful symbol of liberation from white minority rule, attracting loyalty from millions of South Africans who remember life under apartheid.

But after winning election after election for 30 years, the ANC party led by President Cyril Ramaphosa, is now facing its biggest challenge since taking power in 1994, potentially…