Answer:
They are usually Priests or Nuns so the problem well- solves itself. I once went to a Church-operated camp. All of the counsellors- except the Basketball Coach were church brothers, the top end directors of the Camp were Priests. and 6 Dominican sisters formed the Medical staff. They normally do not want people from other denominations to teach in Church-related schools. This was in the past even extended to wholly secular subjects such as mathematics. If you are qualified as a Teacher- and want to teach in a Catholic school- it makes sense to keep and practice the Faith. I know of a number of examples- if you are out there- Ride the Grace Line.