Fugard never mentions apartheid in this play. Why not?

One could argue that, as with any good dramatist, Fugard wants to get his message across by showing, rather than telling. In other words, he doesn't need to state explicitly that his play is about life in South Africa under apartheid; it's more effective to show the effects it has on people in this society.
Also, Fugard seems anxious to make a general point about racial hatred, and, more specifically, about its origins. Although the action of the play takes place in 1950s South Africa, it could just as easily take place at any other time in any other place. Fugard is dealing with universal themes here: not just the origins of hate but also how people of different races can put aside what divides them and try to find a means of living together in relative harmony.
Apartheid, however, is resolutely specific to a particular time and place and would therefore have greatly lessened the impact of Fugard's universal themes. Invoking apartheid as a theme would undoubtedly have turned MASTER HAROLD...and the Boys into a problem play, powerful but transient. And that would've defeated Fugard's dramatic intentions and made for a much less effective play.