If the terms of employment, the handbook, etc., are clear about the morals and ethics of the employees, she id bound to either abide by them, or not be employed there. If there is not that understanding in the terms of employment, then it seems a difficult task to defend the firing.
Additionally, I’m not sure a university such as this falls under the ministerial exception, or even if the university considers its professors as ministers.
© Since the passage of Title VII of the Civil Rights Act of 1964 and other employment discrimination laws, the Courts of Appeals have uniformly recognized the existence of a “ministerial exception,” grounded in the First Amendment, that precludes application of such legislation to claims concerning the employment relationship between a religious institution and its ministers. The Court agrees that there is such a ministerial exception. Requiring a church to accept or retain an unwanted minister, or punishing a church for failing to do so, intrudes upon more than a mere employment decision. Such action interferes with the internal governance of the church, depriving the church of control over the selection of those who will personify its beliefs. By imposing an unwanted minister, the state infringes the Free Exercise Clause, which protects a religious group’s right to shape its own faith and mission through its appointments. According the state the power to determine which individuals will minister to the faithful also violates the Establishment Clause, which prohibits government involvement in such ecclesiastical decisions.