It's wrong to descriminate against someone for a job or acceptance to a school when they should be accepting you/hiring you based on other characteristics.
Why? You're presupposing some set of "correct" criteria on which you should judge applicants to, say, a school, but there is no such set of exactly right criteria (should a university admit the best performing applicants, or the people who will benefit most from going that university, or perhaps the people for whom attending university would be best for society as a whole?) and even if there were it would be impossible to accurately measure it. Arguably race is the exact criteria they should be taking into account -- in fact, that's literally the argument behind affirmative action.
This is why I always find this line of discussion fundamentally naive -- you have to be pretty disconnected from the reality of racism to think that it's some sort of facile moral commandment that drives people to act against racism. If people weren't being robbed of their liberty, their opportunities and their identities, I really wouldn't care what people THOUGHT.* We're not concerned with hypothetical moral problems, but with real and present societal ones.
* this is not to discount the effects of racist thought processes on actions, obviously, but merely to pose an impossible hypothetical in which society remains equal regardless of individual actions