Nowadays it seems Catholic schools have relaxed their standards somewhat. At least when it comes to certain things like dress codes. I saw a picture of my friend's daughter from her homecoming last week and let's just say the dress would have never been allowed when I was in school. Neither would the others that were her daughter's friends. Super short and bare midriffs.... at a Catholic Homecoming Dance. If there were any nuns left, they'd be shocked. Lol.
I can believe that lay teachers would introduce thought-provoking subjects to their students.
I think you are right with the difference between atheists and agnostics. Then there's the differences between Roman Catholic, Russian Orthodox, Greek Orthodox, Protestant, Baptist, Mormon, Episcopalian.... shall I go on? Lol