The short of it is that the ACLU consider affirmative action a form of just racism. This form of racism corrects for past transgressions, helps achieve diversity targets, and "keeps the doors open" for minorities, so they consider it not only morally justifiable, but commendable.

Their position paper on affirmative action is available here: https://www.aclu.org/other/affirmative-action-aclu-position-... and I think it illustrates not only their rationale, but the tone of their support for that philosophy.

Fair disclaimer that I am obviously opposed to this approach and have been cautiously skeptical of the ACLU for a while now.