ANTI-APARTHEID PROTESTERS notwithstanding, the United States will play South Africa in Davis Cup tennis in Nashville two weeks hence. That's been settled on the reasonable basis that if you play by the rules - and the Davis Cup parent group hasn't determined that South Africa has not - then you play tennis. The large demonstrations planned for Nashville don't thereby lose their point. They can be useful in showing that popular feelings against apartheid run high.

But there's a deeper reason why the matches should go on. It touches the larger continuing effort to read South Africa entirely out of the Davis Cup, as it has already been read out of almost all other important international sports competitions, including the Olympics. The reason is simply that in South Africa sports is one of the principal arenas in which "enlightened" whites are trying to soften the workings of apartheid, or racial separateness, and let human beings interact in a normal and civilized way. Foreign critics who slap South Africa down when it stands pat, and when it tries to improve, cannot expect much of a hearing in Johannesburg. It's not just a question of being fair but of being effective.

There is a respectable point of view holding that in a society so fundamentally unjust, trivial changes made largely for foreign consumption aren't worth encouraging. By this reasoning, the tentative success South Africa has had in making both clubs and games at home multiracial, and the substantial success it has had in fielding multiracial teams for international competition, are meaningless; and the presence on the current South African Davis Cup team of a nonwhite player, a first, is tokenism, and in the world's eyes, a gesture meant to buy apartheid the comfort of international legitimacy.

We hold, more hopefully, a different view. We think that foreigners demanding to influence the internal development of South Africa can't afford to sell short the few areas of public life where some progress toward a more humane policy is visible. In sports, nonwhites are getting opportunities to be treated on their merits - something not to be under-estimated in that racist place. In putting policy into effect, if not in shaping policy, nonwhites are being regularly consulted - again, something all too rare in what is for nonwhites a police state.

South African sports policy is a product of modest enlightenment made devious by the demands of political discretion: The right wing wants the sports minister's head. The policy is ahead of national custom; it is pulling custom along. While no realistic observer expects sports to be the engine pulling the whole society, no sympathetic observer should want to derail the sports train. International pressure should be kept on. It's useful to the reformers, though they won't say so. All the same, to help them more, South Africa should be allowed to play.