Final answer:
The Daughters of the American Revolution (DAR) apologized for their segregationist policies after they refused to let Marian Anderson perform at Constitution Hall. Eleanor Roosevelt's actions, including resigning her membership in the DAR and arranging for Anderson to sing at the Lincoln Memorial and attend a state dinner at the White House, caused this shift in approach.
Step-by-step explanation:
The event that caused the shift in approach by the Daughters of the American Revolution (DAR) was when they refused to let Marian Anderson perform at Constitution Hall and Eleanor Roosevelt, the first lady, resigned her membership in the DAR and arranged for Anderson to sing at a public concert on the steps of the Lincoln Memorial. This public action by Eleanor Roosevelt and the subsequent state dinner at the White House in honor of the king and queen of England put pressure on the DAR to apologize for their segregationist policies.