The Supreme Court wrestled Wednesday with the appropriate role for religion in government in a case involving mainly Christian prayers at the start of a New York town’s council meetings.

The justices began their day with the marshal’s customary plea that “God save the United States and this honorable court.” They then plunged into a lively give-and-take that highlighted the sensitive nature of offering religious invocations in public proceedings that don’t appeal to everyone and governments’ efforts to police the practice.