Well, 1ke gave you the answer. I’m not sure I can expand on it other than to say that’s the way it is. It really does depend on the diocese. I know some dioceses who have it in the contracts of the Catholic school teachers that they must be a practicing Catholic in good standing. Thus, if a teacher decided to move in with his/her girlfriend/boyfriend, it would be grounds for termination. Not every diocese is like that, though.
In my diocese, all the Catholic school teachers are expected to go through catechist certification regardless of whether or not they teach religion specifically. Of course, then it falls to the individual principal and pastoral administrator as to whether this expectation is turned into a requirement.