For me regards Catholicism in particular, it’s two things.
One, we consider faith in God to be a start rather than the end-all and be-all. It was not unusual to be expected to attend Bible study as a child and by that I honestly mean actual study, and you were also expected to behave in a way that made you grow closer to God. It’s why the Sacraments are a big deal, because they’re codified things that help you form a bond with God, and why things like charity and public works are often considered a life goal.
Two, sanctity of life is a big thing. I know that abortion gets all the spotlight, but it’s actually a whole package of sorts with Catholicism, in that they’re also often anti-death penalty, pro-healthcare and especially finding cures for usually terminal diseases, pro-gun control, pro helping needy people afford food and shelter, etc.
So the upshot that is a character who’s all about blind unquestioning faith, puts little effort into living according to the teachings and Sacraments, and killing evil people, is all about as opposite from the modern ideal Catholic as you can get.