King David certainly wouldn't have been a good catholic...he wasn't even the best Hebrew when it came to observing the Mosaic laws...yet the Bible says his sins were forgiven and that he was "a man after God's own heart"...him a murderer of the husband of Bathsheba and guilty of adultery with her....David the ancestor of Jesus Christ...
The Catholics would have never granted him absolution(well maybe in the 15th century if he had paid enough indulgence money) but God surely did!
Yes, the Bible is full of this and it is so reassuring. One of my favorites is Peter's denial of Jesus - now that's pretty big-time. Having been raised a Catholic in a very orthodox Catholic home (both parents were converts) I received a strong grounding in the beautiful liturgy and the mysticism of the Church, which I totally respect. Unfortunately, I found the Church very unforgiving when life thrust some unexpected, and unwanted, turns into my path. I experienced it as kicking a person when they were already down, but that was just my experience - doesn't mean it's universal.