The person you're replying to is making the argument "Would you object to a book publisher that only signed writers who were white" or "Should a coffee shop be allowed to only hire white barristas". Which is a sound logical argument if you ignore the entire history of racism in the United States.
That’s a common misconception. Nobody serious has ever doubted that the Civil Rights Act creates a colorblind system. Any contrary treatment has always been justified as exceptions. Even Lawrence v. Bakke in 1973 struck down the racial preferences at issue in that case: https://en.wikipedia.org/wiki/Regents_of_the_University_of_C....
I think people got this misconception that affirmative action was legal because universities practiced it. But the EEOC guidance for example has been consistent since the Carter administration. “Under Title VII, there is no separate legal concept of ‘reverse discrimination.’ Discrimination against any individual on the basis of race, color, religion, sex, or national origin violates Title VII.”
The only exception was that employers who had practiced segregation could take measures to undo the effects of that in their workplace. That’s what “affirmative action” meant. It was not sanctioned as way to address perceived disparities in society at large.