The Department of Justice has said that the school's decision was protected by the First Amendment.
"This case presents an important question: whether a religious entity's interpretation and implementation of its own religious teachings can expose it to third-party intentional-tort liability. The First Amendment answers that question in the negative," a Justice Department statement of interest said.
It added that "religious employers are entitled to employ only persons whose beliefs and conduct are consistent with the employers' religious precepts, and, more broadly, that the United States Constitution bars the government from interfering with the autonomy of a religious organization."
In June 2019, the archdiocese said of teachers that "it is their duty and privilege to ensure that students receive instruction in Catholic doctrine and practice. To effectively bear witness to Christ, whether they teach religion or not, all ministers in their professional and private lives must convey and be supportive of Catholic Church teaching."
Archdiocesan policy states that every Catholic school, archdiocesan and private, must clearly state in its contracts and job descriptions that all teachers are ministers of the Gospel and must convey and be supportive of all teachings of the Catholic Church.
In a June 2019 statement, the archdiocese explained that teachers at Catholic schools are considered ministers, as part of the schools' mission to forming students in the Catholic faith.
"To effectively bear witness to Christ, whether they teach religion or not, all ministers in their professional and private lives must convey and be supportive of Catholic Church teaching," the archdiocese said.
Archbishop Thompson has stressed that Joshua Payne-Elliott was removed not because he is homosexual, but because he had contracted a same-sex marriage, in opposition to Church teaching on marriage.
All people should be treated with love and respect, and sexual orientation in itself is not sinful, the archbishop said.
However, he added, the Church is clear in teaching that the proper role of sexual activity is within a marriage between one man and one woman.
The problem in cases such as Brebeuf and Cathedral, he said, "is about public witness of Church teaching on the dignity of marriage as one man and one woman. That is our Church teaching."
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"In this particular case we're dealing with, those are ministers in our Church. Teachers, guidance counselors, other leaders, leaders of the schools and other leaders in the archdiocese are bound to live out these principles."