CANTERBURY, England — As he passed through the heavy wooden doors of this city’s ancient cathedral behind a procession of 650 other Anglican bishops and archbishops on Sunday, the Most Rev. Rowan Williams, the archbishop of Canterbury, appeared taut and ill at ease. It was as if keeping a church with an estimated 80 million followers around the world from breaking apart over the issue of gay priests and bishops was proving almost too heavy a burden.
The gathering, the Lambeth Conference, takes place once every 10 years. This year’s meeting, centered on two weeks of debate that begin Monday, is taking place only a few weeks after a group of bishops from the church’s traditionalist and evangelical wings, meeting in Jerusalem, founded a new group, the Fellowship of Confessing Anglicans, that many in the church regard as posing the gravest threat of a schism in the worldwide Anglican Communion since...