When my DW taught in Catholic Schools, the way they handled it was that non-Catholic teachers had to uphold Catholic teaching or, if a question came up, that the non-Catholic teacher would refer the child to a Catholic teacher. (For example, a non-Catholic teacher was required to support Catholic teaching on sex, abortion, marriage, etc.)
For conduct, they were held to the same standard as Catholic teachers, while on school business. While off duty, the standard morality clause applied: don't bring scandal. Nobody's going to check to see if they are living with their boyfriend, but don't bring attention to it. Nobody's going to see if they have a prescription for the pill. But don't draw attention to it. And so on. (While Catholic teachers were called to be active members of a Catholic parish, obviously that didn't apply to non-Catholics)
Thanks, that’s very informative.