As an example of how such discrimination can be rational and indeed reasonable...

You have a resume. It provides some noisy data about someone. Including that person's race. Let's trim it down. You have an IQ test result and the person's race. Let's say that two candidates has the same IQ in the test, but one came from a group known to have a significantly lower IQ on average.

If we assume that an IQ test result has any measurement noise - and they do - then the Bayesian conclusion is the candidate from the group with higher average IQ is likely to actually have a higher IQ.

Now resumes constitute very noisy data. People often even lie in their resumes. There are large differences between groups in the US. The dispute is about the reasons for the differences not whether they exist.

A study would need to overcome these effects to demonstrate irrational discrimination. They would need to show that e.g. there was consistent out-performance for the group discriminated against post recruitment.