Boer families were treated terribly by the British during the war (concentration camps etc.). This coupled with earlier fighting with tribes must of influenced Afrikaner thinking?
From the time the Dutch landed (around 1650) on Cape Coast there was an unoffocial Apartheid system between East India Company men, free white's and blacks. The colony started expending slowly with Boers traveling east. There where frequent small ''wars'' between the boers and the natives.
From the 1800s they started converting a part of the native population. These gave rise to the first problem. Some white's did not want to celebrate the Holy Supper with blacks. On the synode in 1857 the reformed state church decided that white's had the right to not celebrate the Holy Supper with blacks. The first pre-apartheid law came out of the church. The church has always been a big part of Afrikaner identity. The idea of white superiority, (old testament )christianity merged together in boer culture. They compared themselves to the jews looking for their homeland. The Orange river became their Jordan river etc. In short they saw themselves as ''chosen'' people, protecting their white/christian culture against a majority of blacks.
The Afrikaners boers where never rich. Al they had was their land and their small belongings. When the English took over the Cape Colony more and more Afrikaners travel east, Afrikaans/Dutch as a language became a big factor of their identity.
After the two boer wars, most of the boers where broke. They lost everything they had and moved to the city's to form white ghetto's. To fix this problem Apartheid was ''started''. It was foremost a system to help the poor white's to get jobs/fix their economic downfall. That is the reason that most of them got to work for the government. While the English where mostly in business. That is the reason that the hardline pro-Apertheid boers are still mostly found in the East of South Africa. The region that was hit the hardest by the wars.
So in short: Apertheid was mostly an economic system after the economic downfall because of the Boer Wars. Given a christian validation by linking it to the story of the tower of Babel (Genesis 11). The Boer wars certainly had influence, because they bankrupted a lot of Boers. But saying that without those wars it would not happen would be a big strech. They where always unofficial Apartheid laws, after 1948(IIRC) it became official policy. It had a lot of support from the Afrikaner population, and the English in power where ''happy'' enough to go with this Afrikaner thinking.
Edit: I am not an native speaker so forgive my spelling mistakes.
Sources (in Dutch and Afrikaans):
.C. Adonis, die afgebreekte skeidsmuur weer opgebou. Die verstrengeling van die sendingbeleid van die Nederduitse Gereformeerde Kerk in Suid-Afrika met die praktyk en ideologie van die Apartheid in historiese perspektief, Amsterdam 1982.
Ras, Volk en Nasie Volkereverhoudinge in die lig van die Skrif. Goedgekeur en aanvaar deur die Algemene Sinode van die Nederduitse Gereformeerde Kerk Oktober 1974,2e druk, Kaapstad 1977.
J. Kinghorn. In: Identity in Southern Africa. Journal of Southern African Studies. Vol. 20 no. 3, 1994