Ms. Barrett told the senators that she was a faithful Catholic, and that her religious beliefs would not affect her decisions as an appellate judge. But her membership in a small, tightly knit Christian group called People of Praise never came up at the hearing, and might have led to even more intense questioning.

Some of the group’s practices would surprise many faithful Catholics. Members of the group swear a lifelong oath of loyalty, called a covenant, to one another, and are assigned and are accountable to a personal adviser, called a “head” for men and a “handmaid” for women. The group teaches that husbands are the heads of their wives and should take authority over the family.

Current and former members say that the heads and handmaids give direction on important decisions, including whom to date or marry, where to live, whether to take a job or buy a home, and how to raise children.

Legal scholars said that such loyalty oaths could raise legitimate questions about a judicial nominee’s independence and impartiality. The scholars said in interviews that while there certainly was no religious test for office, it would have been relevant for the senators to examine what it means for a judicial nominee to make an oath to a group that could wield significant authority over its members’ lives.