There are frum people who work in Catholic schools. I know a frum woman who did P3 tutoring in the morning in Catholic schools and in the afternoon in Jewish schools. Guess which kids were better behaved?
I suspect there are frum teachers who actually work for Catholic schools. Obviously, they don’t teach religion, but math is math.
I know of a girl from a MO background who was hired by a BY day camp. She dressed and acted appropriately. Some of her campers eavesdropped on a conversation she was having with another staff member in which she mentioned movies. From that time on, her campers (little BY girls, maybe 1st or 2nd graders) tormented her, calling her all kinds of nasty names, making her cry.