Bobby Kennedy at the behest of John, got MLK out of jail 3 weeks before the 60 election. He did this to try and appeal to the million new black voters. He and his brother knew that if they could get that vote, it would be a very powerful voting block especially in the south. After the election, the new administration quickly lost the battlecry of equal rights until 6 kids were killed in MS, then, owing to the looming PR disaster Bobby then provided protection.
Bobby and company risked a nuclear confrontation with the USSR to try and assert their control over the military. They were willing to risk a war so long as their agendas were followed.