I don't see how it would be unconstitutional, but it would probably be illegal per the civil rights act.
Though now that you mention it, I looked at the article a bit more closely. It says that conservatives "...argued that the Constitution and the civil rights law prohibited discrimination based on race...". The civil rights law part makes more sense than the constitution part. But, the article says that the SCOTUS based this on the 14th amendment.
It's probably more complicated than this article makes it out to be.
