Following the Civil Rights Act of 1964, the federal government tried to put pressure on the LDS Church to quit discriminating against blacks with regards to the ban on priesthood.  A Civil Rights investigation was opened to see if BYU was in compliance with the Civil Rights Act.  Dr. Matt Harris describes the results of that investigation.

Matt:  The timeline is important. So April of 1968 is when they mail the civil rights letter, the letter to [BYU] President Wilkinson. This is the Office of Civil Rights in Denver, Colorado. They’re an arm of the Justice Department. Just a little context here, the Lyndon Johnson administration, in the 60s, decides that they’re going to go after private high schools and universities that discriminate against African Americans. So that’s a priority for the Justice Department in the Lyndon Johnson administration.
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[Wilkinson] knows that if it ever went to court that if BYU were to sue the federal government for violation of their religious rights, they would lose. He knows this because it’s going on during that time.  Some Christian universities are suing and losing. So there’s case law that’s been built up in favor of the Justice department.
So he knows what’s going on, and he knows if he goes to court, he’s going to lose. But he has the board, and the board of trustees is comprised of the apostles, most of them are apostles.  These guys are, most of them are conservative, and they don’t like being told what to do.
Oh, my goodness! So, the federal government telling them how to run their school, that is just way too much for them. Harold Lee is another one. “How dare they tell us what faculty to hire?” He says that.”We’ll shut this place down if we ever have a negro student,” he says. I mean, they’re defiant. They’re belligerent, and so poor Wilkinson is caught right in the middle of the Civil Rights investigation and this recalcitrant board that doesn’t want to be told what to do.
Check out our conversation….
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347: Did Nixon & Carter Pressure BYU Over Race?