That has been a policy dispute for many years, going back at least to 1980 as Indiana University professor Fabio Rojas reminds us in this Martin Center piece. In it, Rojas argues in favor of an open-doors policy, treating children of undocumented immigrants no differently than anyone else.
People should be judged on their behavior, not the behavior of others. To exclude students from colleges because of a legal violation by their parents directly contradicts this central idea. If a student attends school, participates, and masters the material, then they should be appropriately rewarded. If conservatives oppose affirmative action because it rewards applicants whose credentials fall below a school’s standards, they should also support undocumented students who meet and surpass the school’s criteria for admission and financial support. To do otherwise is a rejection of meritocratic norms.
Rojas sums up his case:
We have a choice. We can go against important values, exclude undocumented persons from education, and thus create a student population segregated by national origin and legal status. Or we can allow them to participate in the American project. We can invite them to join our community, be educated in our schools, and renew our nation—as have generations of immigrants before them.