Brophy ran against Lewis for President of the UMWA in 1926 on a "Save the Union" slate, calling for nationalization of the coal industry. He probably would have won the election if the vote had been held democratically.
Lewis drove Brophy and his supporters from the union after his victory in 1926. More specifically Lewis accused Brophy of dual unionism, based on the support that he had received from the Trade Union Educational League, an arm of the Communist Party which had supported his candidacy. The CPUSA later burned its bridges with Brophy, denouncing him as a reformist, after it adopted a policy of opposition to mainstream unions during the "Third Period".
Brophy was a self-educated man, who spent his time after Lewis' expelled him from the UMWA studying economics and philosophy. He was also deeply religious, relying on "Rerum Novarum", the papal encyclical of Pope Leo XIII supporting the right of workers to form unions, as the bridge between his faith and his commitment to the rights of workers.
Lewis' successor, Philip Murray, named him the Director of Industrial Union Councils. That position proved to be an important one in the expulsion of CP-led unions from the CIO following World War II. He was one of the strongest advocates for centralized control of the CIO's political action committees and the industrial councils, which were made up from delegates from the more or less autonomous unions affiliated with the CIO but which were themselves creations of the CIO, obliged to follow CIO policy imposed from above. In 1948 he led the crackdown on local labor councils and state bodies within the CIO that had endorsed Henry Wallace or opposed the Marshall Plan in contravention of national CIO policy.
Brophy also served as a CIO representative to international labor organizations such as the World Federation of Trade Unions and the International Confederation of Free Trade Unions and as a labor representative on a number of government agencies, such as the National War Labor Board, the Committee on Fair Employment Practice established by Executive Order 8802 and the Wage Stabilization Board. He continued serving with the AFL-CIO after the CIO reunited with the AFL in 1955.