Criminals? I think there may be some confusion here. Some "illegal" immigrants are criminals ... the ones who commit crimes. But merely being in this country without proper documentation is not a crime. You cannot be "convicted" of being an illegal immigrant. It violates no criminal statute I know of. True, the government has the power to remove such people by initiating civil proceedings against them, but that doesn't make them criminals. They could not be charged with violating any criminal statute by a prosecutor or grand jury, and they could not be prosecuted for committing any offense punishable by fine or prison sentence, merely because they are in this country.
I think that's an important distinction, because many "illegal" immigrants have done nothing wrong except be born to parents who brought them from Mexico (or another country) to the U.S. without proper documentation. If ND believes that there are kids in that category who are likely to be successful and worth investing the university's resources in teaching and training, why not let them in?
I've noticed a lot of people on this board treat admission to ND like a reward for good moral conduct. I could be wrong but I don't think that's how ND's admissions people look at it. I think most admissions professionals look at a student as an investment opportunity ... is this person likely to be successful and someone that we will be proud to call a ND graduate someday? That your parents may have done something that you are politically opposed to really doesn't have much bearing on that question.
Suppose you have a kid like that ... brought to the U.S. at the age of 5, worked hard in school, proved to be an exceptional student, crushed his ACT, stayed out of trouble, earned a scholarship to college. This kid's done nothing wrong. If ND thinks he is likely to be a successful person, why shouldn't it admit him?