O'Riordan was one of the founding members of the Irish Workers' League in 1947, with both she and her husband actively involved in the organisation. She negotiated being both a devout Catholic and a communist, having to seek out a priest, in Whitefriars Street Carmelite church, who was a sympathetic confessor. She was an active member of the Irish-Soviet Friendship Society and later the Ireland–USSR Society. While sympathetic to the USSR, she was also critical of them, including the suppression of the Hungarian uprising in 1956. She opposed all forms of antisemitism, and was involved in the activities of the Irish Jewish Museum and the local Jewish community in Portobello, which was close to her home. She was also involved in the anti-apartheid movement, and was involved in a number of campaigns for civil rights and the improvement of social conditions. She was active in children's literacy programmes, and in the assistance of refugees from Chile fleeing the Pinochet regime.