I think they can legally discriminate based on income but not on race, sex, etc. Up to this point we haven't had to have laws restricting employers from hiring based on income, because they've never wanted to. If it became a common practice, however, I think it should be made illegal because children are not responsible for the income level of their parents. Think of the Cultural Revolution in China; income-based reverse discrimination can be very ugly.
It is a repugnant policy, but I hardly think its anything new. I have a family member who worked in an Ivy league admissions office in the 1980's and says that it was absolutely accepted fact that being a white male from a comfortable background was a strike against any applicant. Such people were considered uninteresting unless they were just stratospheric in terms of grades, scores or other achievements (linebacker, flutist, dad donated a building etc.)