First, let's sharpen the question. Although the apartheid issue was typically framed as one of equality and justice, it was also a matter of freedom; black South Africans - and many whites - were horribly unfree. We might laugh at Thomas Hazlett calling apartheid socialism with a racist face, but if you're the sort of silly libertarian who equates socialism with statism, it's not so daft. This poses the question: why were Tories so vocal in demanding freedom for Russians, and so quiet about demanding it for Black South Africans?
When Thatcher died, the Economist called her a "freedom fighter". It didn't have South Africa in mind.
You might think there's a simple reason for this: Tories were racist. Whilst this might be true for the more extreme sympathizers with apartheid, I can't believe it's true for all Tories. And the issue here is not simply that a few actually sympathized with apartheid. Very many more Tories were quiet on the issue. I took an interest in the anti-apartheid movement in the 80s, and it certainly wasn't overcrowded with Tories.
Another possible explanation is that Tories were never really much interested in freedom. What they supported was capitalism - in its basest sense of a system which makes profits for a few by the exploiting the many. And South Africa had capitalism, Russia did not.
One is a form of homophily. To a certain type of person in the 70s and 80s, white South Africa was a very congenial place, if you ignored a few things. And we naturally tend to take our political views from people we feel sympathy with.
The other is simply "my enemy's enemy is my friend". The apartheid regime presented itself as a fighter of communism. And in the simple manichean world of the cold war, this was enough for it to get the sympathy and support of the right; the same, of course, was true for Pinochet.
But here's the thing. These motives were - of course - not confined to Tories in the 70s and 80s. All of us, to some degree, have an element of tribalism in our political views; given bounded rationality and knowledge, it can't be otherwise. And "my enemy's enemy" is - as Nick Cohen will tell you - one motive behind the sympathy some (a few?) leftists have for reactionary Islamism.
In this sense, whilst many Tories were wrong on apartheid, the reasons for that error were not confined to them. The Tories' embarrassment about South Africa should warn us all that our political opinions can be formed in some non-rational ways.