I went to a Catholic high school. It wasn't my choice. Like most people of the pre-millennial generations, I didn't have those "You go ahead and decide what you want" parents. My dad went to Catholic schools in Chicago as a young Polack, and such would be my lot as well.
The Covington Catholic story prompted me to think about the place I went a little more fondly. I have no memories at all of getting right-wing political messaging from the priests, nuns, or lay teachers there. Conversely, there are many clear memories of adults telling us things like "You are all very sheltered" and "You're here because your parents can afford to send you here." Our "World Religions" course, often a propaganda nightmare at Catholic schools, actually taught me some things about the world's major religions.
The thing is, it wasn't overall a Good School in any meaningful sense even though adults constantly referred to it as a Good School. I graduated barely knowing any math. It offered 3 AP classes, while the nearby public schools had a dozen. One of the teachers told us (in 1995) her salary was under $20,000. Many of the teachers were priests or nuns who had no formal training in teaching. The sports-first culture of the school was cloying.
What was clear throughout, even to people as young and naive as we were, was that going to Catholic school was above all about whiteness. Parents (not only my own, but the peer parents as well) were explicit about this. Because while I have no memories of getting right-wing indoctrination from adults at school, I remember a lot of it coming from my classmates' parents. We were sandwiched between Joliet and Chicago, and my high school was "safe" unlike the public schools (which, statistically or subjectively, are not dangerous schools by any measure). Those schools had "gangs," were "dangerous," or simply were "bad," all of which were such transparent code words that even 14 year-olds knew what they meant: they had black kids, Hispanic kids, poor kids, etc.
My school was not exclusively white, of course, but the cost of entry ensured that the black and Hispanic kids were sufficiently "good kids" from "good families." The Covington example seems to be one in which school officials – one priest in particular – were indeed giving the kids a heavily MAGA political message. But among Catholic schools around the country I'd be stunned if that was the norm. The Fox News rhetoric isn't coming from priests and teachers; it comes – in unbelievably heavy and consistent doses – from the kind of parent who insists that their kids attend a Catholic school. A scattered few probably have deeply held Catholic beliefs behind that motivation, and those become apparent as students get to know one another and the families. Much more common are the families who don't seem to know or care that the nearby public schools have better facilities, more "college prep" options, and in some areas far more funding. They simply want to make sure their kids, who are very Good, go to school exclusively with other Good Kids instead of the riff-raff and "Gang Bangers."
Your experience may vary. Mine was unambiguous.