I think of it as a four-step process. Take Sonia Sotomayor, for a not-currently-controversial example. Step one is that she can't be a Supreme Court justice because she's hispanic. Step 2 is, she's hispanic, but she can be a Supreme Court justice anyway. Step 3 is that she's nominated to be a Supreme Court justice, and nobody mentions that she's hispanic. Step 4 is that, when she's nominated for the Supreme Court, people mention that she's hispanic, but in the same way that they mention that she was born in the Bronx - as background personal-interest information, not as a "does that disqualify her or not" issue.

The US started at step 1. It's moved to step 2. My personal impression is that it was moving to step 3, though I'm sure that at least some people will disagree. But it seems to me that the current progressive approach is dragging us back to step 2, not moving us toward step 4. And I think that the older approach, what you call "a framework in which the prescription for making sure historical instances of racism don't repeat is to banish race as a category from human thinking and discourse as far as possible", would have gotten us at least solidly to step 3, and maybe eventually to step 4.

I don't think dragging everything back to step 2 is progress.