In the LDS Church, Bangerter served as a bishop in Granger and was later president of the church's North Jordan Stake. From 1958 to 1963, Bangerter was president of the church's Brazilian Mission. After serving in Brazil, he became a regional representative. In 1974, he became the first president of the church's PortugalLisbon Mission. In 1975, he became an Assistant to the Quorum of the Twelve Apostles. In 1976, when the position of Assistant to the Twelve was abolished, Bangerter became a member of the First Quorum of the Seventy. He twice served as a member of the Presidency of the Seventy, from 1978 to 1980 and from 1985 to 1989. In 1989, he was designated as an emeritus general authority and released from active duties.
Bangerter was the father of 11 children. In 1944, he married Mildred Lee Schwantes, with whom he had four children. Mildred died of leukemia in 1952. In 1953, Bangerter married Geraldine Hamblin and they became the parents of seven children.