Alexander was active in the socialist and trade union movements. In 1934, politicized by the Great Depression, Alexander joined the Young People's Socialist League, the youth section of the Socialist Party of America. He continued organizing activities for YPSL while at Columbia and remained an active member of its parent group, the Socialist Party of America, serving as a member of its executive council 1957 to 1966. When the Socialist Party changed its name in December 1972 to Social Democrats, USA (SDUSA), he maintained his membership until 1980; according to Perrone's biographical sketch, Alexander thought that SDUSA had become "too conservative".
It was as a leader of the New Jersey YPSLs that he first met Jay Lovestone, then head of the Communist Party, Opposition. Alexander would later go on six missions to Latin America for Lovestone, first under the auspices of the Free Trade Union Committee, then under the direction of the AFL-CIO International Department.
Alexander was a member of the Board of Directors of the Rand School of Social Science from 1952 until its closure in 1956. He served on the League for Industrial Democracy's National Council and was an active member of Americans for Democratic Action and a delegate to several of its national conventions.
During the 1950s, Alexander served as a consultant for the American Federation of Labor and AFL-CIO on the organized labor movement in Latin American and the Caribbean. In 1961, he was named by president-elect John F. Kennedy to the Task Force on Latin America, which recommended the establishment of the Alliance for Progress.
Alexander was also a lifelong member of the Council on Foreign Relations.