This is the real issue. It's easy to talk big, but once you run up against the Constitution in such an obvious manner, it gets tricky. The NCAA was stripped of a lot of its power in a single disastrous session in front of the Supremes. This issue straddles the Freedom of Association issue in a fashion similar to the NCAA telling student athletes that their names, were, somehow, not they're names??? For Constitutional scholars, arguments like this are just a hard sell.

Not sure what the solution is? But as long as we're going to allow private universities, we're going to run up against the issue of them expressing the rights any other private organization would express. Maybe taxes might be a way to compel cooperation? It's clear however, that traditional legal remedies won't have teeth in the face of the First.