We already live in that kind of society.

It's just that the sorting mechanisms are drastically more crude than a DNA test.

The best sci-fi, like Gattaca, aren't great just because they present an interesting possible future to work toward or avoid, but because they exaggerate and lay bare the problems we already have in the present that are simply harder to recognize. The world of Gattaca already exists, by way of racism, sexism, caste systems, cultural and religious discrimination, etc. In fact, the film says exactly this in the open scenes with "we now have discrimination down to a science".