"As Amoris Laetitia notes, bishops must arrange for the accompaniment of estranged and hurting persons with guidelines that faithfully reflect Catholic belief," he said, citing paragraph 300 of the Pope's document.
That passage stressed careful discernment that does not avoid "the gospel demands of truth and charity, as proposed by the Church." It stressed the need for "humility, discretion, and love for the Church and her teaching" for discernment for those in irregular marital situations.
The divorced-and-remarried are invited to attend Mass, pray, and take part in parish activities. Their children should be brought up in the faith and are "integral to the life of the Catholic community."
Cohabiting couples without children should domestically separate to prepare themselves for marriage. Those with children may have to live together, for the children's sake, "but in chastity."
For those with same-sex attractions, Church ministers should emphasize "that they are loved by God, that Jesus desires them to receive an inheritance as adopted sons and daughters of the Father, and that, as with every Christian, this is made possible through the gift of grace," Archbishop Chaput said.
Given Christian teaching on marriage and sexual intimacy, those with same-sex attractions are "called to struggle to live chastely for the kingdom of God."
For same-sex couples, the archbishop noted the importance of remembering that some couples "live together in chaste friendship."
"The Church welcomes all men and women who honestly seek to encounter the Lord, whatever their circumstances," he said. "But two persons in an active, public same-sex relationship, no matter how sincere, offer a serious counter-witness to Catholic belief, which can only produce moral confusion in the community. Such a relationship cannot be accepted into the life of the parish without undermining the faith of the community, most notably the children."
Archbishop Chaput noted the "great suffering" of those who are separated or divorced.
There is no obstacle to receiving Holy Communion for those who recognize that their first marriage is indissoluble and refrain from a new union. Indeed, they should receive the sacraments regularly, he noted.
"God is faithful to them even when their spouses are not, a truth that fellow Catholics should reinforce," he said.
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Archbishop Chaput repeated that marriage is permanent, monogamous, and open to life.
"Jesus himself raised marriage to new dignity," he said. "The valid marriage of two baptized persons is a sacrament that confers grace, with the potential to deepen the couple's life in Christ, especially through the shared privilege of bringing new life into the world and raising children in the knowledge of God."
The archbishop stressed the great joy of marriage, acknowledging its stresses and suffering while also praising the grace of the sacrament, which can "strengthen [the couple's] relationship, not just as an idea but as a reality that impacts their daily married life."
One prominent Catholic objected to the archbishop's presentation of Catholic teaching. Philadelphia Mayor Jim Kenney on Twitter snapped that Archbishop Chaput's actions "are not Christian."