The good, upstanding Christian people of Poker Flat are determined to clean up their town in "The Outcasts of Poker Flat" by Bret Harte. They decide that there are four people who must go in order for that to happen.
The Duchess is a prostitute in town, and that obviously not the kind of upstanding citizen the people of this town want to have around. She is a bit of a whiner, but when it matters (as she and Piney are dying) she is compassionate and caring.
John Oakhurst is a gambler, and that is certainly a profession which cannot be condoned by the people of a Christian town--even if the town's name does have the word "poker" in it. We learn that he, too, is a kind and compassionate person, as demonstrated by his earlier association with the Innocent. He is "the strongest and yet the weakest of the outcasts of Poker Flat." When it matters, though, he is kind and caring.
Every indication is that Mother Shipton is the town madame, so it is not surprising that the town wants to expel her. Despite her profession, she is a woman of great dignity and sacrifices herself so that someone younger and more innocent (Piney) can live. When it matters, she is kind and caring.
Uncle Billy is the rapscallion of the group, a drunkard and a thief. He ends up stealing the groups horses and some of their food; his selfish actions cause the others to lose their lives. He is a man no one wants around.
In short, three of the four "undesirables" are, perhaps aside from their professions, the kind of moral and upstanding people a town would want in its citizenry--unlike the townspeople who kicked the outcasts out, in the cold, right before winter, to travel through the mountains, without enough supplies.