Church employees should follow church doctrine
In a Christian school, teachers are the adults who have the most contact with students, and they are most visible representation of church doctrine. If a teacher either does not live according to the church's teachings or teaches students in a way that is contrary to church doctrine, the school needs to correct that problem. If the school does not, it sets a bad example for the students. This is why a Roman Catholic school in New Jersey was right to fire an unmarried woman from her job as a teacher after she got pregnant.
The ex-teacher's attorney claims that the church is supposed to "love the sinner and hate the sin." But that is the point. There are earthly consequences for behavior. One can continue to love and support the ex-teacher, accept her repentance and welcome her into fellowship while also recognizing she set a bad example for students being taught Catholic doctrine on the proper place of sex. The issue is not forgiveness, but the example it sets for the students, from both the teacher and the administration.
One of the objections is that others are not caught for engaging in similar behavior. But the fact that some are not caught does not mean the standard should be destroyed, any more than speed limits should be abolished because not everyone who drives too fast is given a ticket. As far as whether a man can be caught engaging in extramarital sex, of course he can be caught. The evidence may not be as obvious, but it can be revealed if a man's girlfriend is suddenly with child - especially if she tells the school about it.
The basic issue here is the First Amendment. The New York Times claims that this case represents "the highly charged debate over the relationship between the government and religion." But that is the whole point. There should be no "relationship" at all. Churches should be free to hire and fire based on whether someone follows church doctrine in word and practice. The government should not be micromanaging these internal decisions, and the church is a much better interpreter of its own doctrine than the state.