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Walter Weber, an attorney for the American Center for Law and Justice, which filed an amicus brief in support of the church, said the court’s unanimous decision — both the liberal and conservative wings of the court ruled against the agency — could be chalked up to legal overreach by the EEOC.

“You could argue that this teacher was beyond the scope of the ministerial exception,” Mr. Weber said. “The problem with the EEOC brief was that they argued that there should be no ministerial exception at all. … Their argument went way too far.”

The EEOC did not respond to a request for comment, though liberal-leaning church-state separation groups lamented it.

“Clergy who are fired for reasons unrelated to matters of theology — no matter how capricious or venal those reasons may be — have just had the courthouse door slammed in their faces,” said the Rev. Barry W. Lynn, executive director of Americans United for Separation of Church and State.