There are those in Victorian society that would argue the life of a mate is more honorable than the life of a beggar. Not only that, they would rather have the dregs out of sight suffering at sea, than on the streets of London in the public's eye where they would invoke sympathy. There are people, however, of so refined and delicate a nature, that they cannot bear the contemplation of such horrors. Dickens is saying that the upper classes do not mind reading about criminal characters, but they want them to be totally immoral and without any redeeming qualities. However, Dickens realizes that everything is not black and white.
Most criminals live in the gray areas.
They make their best of their lives, like the happy Artful Dodger, even if they would prefer a life of higher standards, a life of an upper class person. The dregs of Victorian society are not the dregs, because they wish to be criminals and love a life of crime. They are the dregs, because this is what society has made them. They have no choice, in order to survive they must beg, borrow, and steal. The fact Dickens would find this reprehensible is obvious considering his mother and father were placed in debtors prison and he was separated from the family.