Interesting point. If the Protestant or Jewish person lived by the principles of Biblical morality, that would cover that issue. However, there are serious theological differences, especially for a Jewish person. Personally, if I were paying for Catholic schools, I wouldn't want there to be a question regarding whether teachers were Christian, except in a special case such as having a Jewish teacher of Hebrew or Biblical Studies.
I would suggest good moral people of any biblical faith tradition could teach mathematics, science, business, English , foreign languages, etc., including whatever morals content a particular course might legitimately contain. The catecism classes should retain good Catholjc teachers and hopefully there wi be enough of them! The non- Catholjc teachers should be guided in the particular Church teachings that may arise in their classes, so that they can avoid making mistakes out of simple ignorance ( ant competent priest or trained supervisory person should be able to do this pretty well). I can say is that there are a number of supposedly - Catholic teachers who definitely should not be permitted to get anywhere near the children anymore ( unless they seriously commit to “cleaning up their acts”). IMHO. A teacher who claims to be catholic- Christian but who supports and evrn participates actively in the moral degeneracy that ( almost) IS San Francisco these days, needs to be replaced ASAP. A retaining such staff does is teach a cesspool way of life, extreme anti- life attitudes, disrespect for the. I me and church teachings, and quite frankly the open hipocracy of putting such persons in the classrooms teaches that — hipocracy - living a lie- is just fine with the Church because, after all, the Church itself does it to the children every day in school by claiming to uphold moral values while putting open homosexuality- advocates and open abortion advocates in to teach the children. Prayerfully the new arch-bishop will be able to clean house
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)
I’ll have to dig deep to find my 1969 contract from when I was hired by my hometown Catholic elementary school to teach social studies to see if any of these were included. I probably told him that I was a member of the local Disciples of Christ congregation that was 3 blocks from the school. I don’t remember if Fr. Pax told me not to do any “protestant recruiting’ or not; he did state that taking my home room students to mass every morning was a requirement and I said that was no problem for me. I know that Fr. Meiring, head of the education department at my college recommended me for the position.