I don’t think there is an underlying message by Scorcese as much as Catholicism was dominant and influential in the NY Gang and Godfather periods. It would be difficult to portray that time period without touching upon the power held by Catholicism.
In The Departed, Deniro’s character definitely carries a chip on his shoulder against the church which seems to stem from his school years, We know now that many of the sexual abuse cases took place in the time frame which would have been the Deniro character’s boyhood, so it’s not as if all members of the Church were stellar representatives of the faith then, or now.
When one is making a film about gangs in society and Catholicism is the dominant religion of the time and geographic area it would be inconsistent to pretend not a single representative of the Church participated in that life style along with the gang members.