We give the Elia Kazan classic from 1954, On The Waterfront, an Edgy rating and a Catholic rating. On The Waterfront was edgy for its time, in dealing with issues of corruption. It is Catholic in having a positive Catholic priest character, and, in the final scene, a Christ-like scene, recalling the carrying of the cross.
Dealing with gritty topics from a Catholic perspective was more common in the 1950's and, On The Waterfront is a fine example from a time when nobody had to try to characterize movies as Edgy Catholic.
You can check out On The Waterfront at these links: