MIT is taking (lots of) money from federal government. That makes them dependent on the government and government is within its right to attach strings to the money.
MIT is free to not do what the government wants but then government is free to stop giving them (our) money.
Furthermore, MIT, like any other organization, must obey state and federal laws.
For example, there's a law that you cannot discriminate in hiring based on sex or religion. If IBM, MIT or a barber shop discriminates it's the role of the government to enforce the law and make them stop. The easy way is sending them a letter and asking. The hard way is to sue them in federal court.