On January 18, 1963, four days after Governor George Wallace's 1963 Inaugural Address (often known as the "Segregation Forever" speech) on the steps of the Alabama Capital in Montgomery, Grafman joined with ten other prominent members of the local clergy in issuing an "Appeal for Law and Order and Common Sense" in which they affirmed basic principles of equality, justice and free speech, but also the need to obey current law.
Reaffirming the January statement, the Call for Unity expressed the view that the planned demonstrations were "unwise and untimely", and that attempts to correct the very real injustices should be pursued patiently in the courts, by local residents.
[3] Grafman believed that he and the other signers of the "Call for Unity" had been unfairly branded as racist by King in his "Letter from Birmingham Jail", but he remained silent about it in public for 15 years.
"[4] Grafman was subject to fairly extensive criticism throughout the rest of his life, including from some within the Jewish community, as a result of his signing of the statement.
Grafman opposed racial segregation, even though he disagreed with King and other leaders of the Civil Rights Movement over tactics and timing.
[5] In his 2001 book Blessed Are The Peacemakers: Martin Luther King Jr., Eight White Religious Leaders, and the "Letter from Birmingham Jail", S. Jonathan Bass cites several examples of Grafman's role in the Civil Rights Movement, including:[5] Richard Arrington, Birmingham’s first black mayor said: "[Grafman] has a high level of credibility among all segments of the community, black as well as whites.