Suitts began work in 1970-71 at the Selma Inter-Religious Project, an organization providing legal and technical assistance to community organizations in southwest Alabama and southeast Mississippi after the Selma March. Among other work, the Selma Project helped to organize some of the first child care centers in the Black Belt and interracial cooperatives among poor woodcutters in the rural South. In late 1972, Suitts became the first executive director of the Alabama Civil Liberties Union, where he supervised a legal program that included several path breaking cases involving fair redistricting, mental health law, gay rights, prison reform, and the closing of the state agency set up earlier by Governor George Wallace to spy on citizens and activists.

During the 1970s, Suitts helped to convince the Federal Communications Commission (FCC) to annul the licenses of the Alabama Public Television Commission, the first time the FCC revoked a broadcast license because of racial discrimination. Suitts also started the Constitution Lobby, the first civil rights coalition lobby in Alabama.