Stigmata: Not only was this movie filled with flat out lies and distortions about the Church, but this movie was filmed as, and marketed as, a horror/thriller, and thus marketed directly to the “late teen” demographic. What a wonderful time to teach them that the church is untrustworthy and corrupt.
The Order: As above, the Church is corrupt and hiding things, but this time, there is an order devoted to destroying supernatural things (actually, this part of the story I don’t mind, but of course it can’t be this simple). In the end, there is an “alternate” way to salvation that the Church has hidden for years, oh, and its so unfair that a Catholic priest has to give up his sex life that its okay for him to break his vows.
And again, it was a horror/thriller, so squarely marketed at teens.
There are others, like John Carptenter’s Vampires, where the (wait for it) secret order of Catholic vampire hunters throws parties with prostitutes to celebrate their victories of a den of Vampires, and the priest assigned to them isn’t really accepted until he starts swearing and cursing.
The irony of it all is I think the idea of the Church having a “monster hunting” division is actually an interesting idea for sci-fi/horror stories, but they never seem to be able to show priests or even faithful Catholics in a favorable light.