Hastings, a grandson of George Woodyatt Hastings, was born in Kuala Lumpur, Malaya, but his mother moved to England to bring up the children when he was little more than a baby. He was educated at Douai School (1943-46) and Worcester College, Oxford (1946-49).
In his final year at Oxford, Hastings discerned a missionary vocation. He joined the White Fathers but later left the order to become a secular priest in the Diocese of Masaka, Uganda.
Hastings studied theology at the Collegium Urbanum, the college of the Congregation of Propaganda in Rome. He was ordained in 1955 and awarded a doctorate in 1958. His lifelong association with The Tablet dates from this period. In 1958 he also obtained a teaching degree from Christ's College, Cambridge and in 1959 he took up his priestly functions in Uganda.
In Uganda Hastings served in pastoral and teaching functions and was charged with interpreting the documents of the Second Vatican Council to priests in Africa. His notes on these documents were later published. He also agitated for a relaxation of the discipline of clerical celibacy in the African context, attributing the low numbers of black clergy to the cultural alienness of this requirement.
In 1966, after bouts of malaria, Hastings returned to England and became active in ecumenical dialgoue through the preparatory commission of the Anglican-Roman Catholic International Commission. He was also commissioned by a number of Anglican dioceses in Africa to prepare a report on Christian and customary marriage.
From 1972 to 1976 Hastings was on the staff of an ecumenical missionary school, the College of the Ascension in Selly Oak, Birmingham.
In 1973 Hastings brought the massacres carried out by the Portuguese army during the Mozambican War of Independence to world attention, first through The Times and later at the United Nations.
In 1978 Hastings came to the decision that as a Catholic priest he was free to marry. In 1979 he married Ann Spence without seeking ecclesiastical permission or resigning from the priesthood. Although this was a clear breach of canon law he was never formally excommunicated, largely because since leaving Uganda he had not been subject to the oversight of any particular bishop. On occasion he continued to exercise his priestly ministry after his marriage.
From 1982 to 1985 Hastings was Professor of Religious Studies at the University of Zimbabwe. From 1985 to his retirement in 1996 he was Professor of Theology at the University of Leeds. From 1985 to 2000 he edited the Journal of Religion in Africa.
Late in life Hastings was active in raising awareness of the atrocities accompanying the breakup of Yugoslavia and the reassertion of Serbian control over Kosovo. He was a founding member of the Alliance to Defend Bosnia-Herzegovina.
Hastings died in Leeds on 30 May 2001 and was buried at St Mary's Church, East Hendred, Oxfordshire.