BTTT!
This is a similar tactic to what law schools used against military recruiting prior to the Solomon Amendment. They basically said that no entity can recruit unless it signs a non-discrimination paper. The military, due to its rules, could not sign it, therefore it was banned from recruiting. Then, the Solomon Amendment was passed which basically stripped federal money away if schools did not allow recruiting. The application of the Solomon Amendment was upheld by the federal Supreme Court in FAIR v. Rumsfeld.