I would expect that the controversial stances of F.W de Klerk would have alienated many white voters who supported apartheid

A referendum on ending apartheid was held in South Africa on 17 March 1992. The referendum was limited to white South African voters, who were asked whether or not they supported the negotiated reforms begun by F. W. de Klerk, in which he proposed to end the apartheid system. The result of the referendum was a large victory for the "yes" side (1.9 million (68.7%) - For and 875,619 (31.3%) - Against).

and would assume the black majority as well as other minorities would have stuck with the ANC

How the ANC's vote was constituted:

African	11.5 million
Coloured	0.5 million
Indian	150,000
White	50,000
Total	12.2 million

How the National Party's vote was constituted:

White	1.9 million
Coloured	1.2 million
African	0.5 million
Indian	0.3 million
Total	3.9 million

The National Party had only limited success in convincing Africans that it had truly moved away from its whites-only past. Only around a quarter of Africans saw the party as multiracial at the close of the campaign. Not surprisingly, the National Party failed to capture many African votes. On the other hand, the National Party did achieve a considerable degree of success at altering its image in the coloured and Indian electorate. These voters by and large bought the party’s claims of transformation and a majority of them supported it, making the National Party the most diverse party in South Africa and giving it control over the Western Cape. The ANC had less success at image change with coloured and Indian voters, many of whom continued to view the ANC as an African-only party.

Source: The Politics of the New South Africa: Apartheid and After, Heather Deegan, 2001; Framing the Race in South Africa The Political Origins of Racial Census Elections, Karen E. Ferree, 2010.