In "The Outcasts of Poker Flat," Bret Harte's primary point concerns judging people based on their hearts and character rather than their outward appearances or, in this case, their professions.
How the outcasts are forced to leave Poker Flat is one of the great ironies of the story.
[The town] had lately suffered the loss of several thousand dollars, two valuable horses, and a prominent citizen. It was experiencing a spasm of virtuous reaction, quite as lawless and ungovernable as any of the acts that had provoked it. A secret committee had determined to rid the town of all improper persons.
A gambler, a drunkard, a madam and a prostitute are all banished from the town because Poker Flat is a God-fearing, Christian town (note the use of the word Sabbath twice in the opening paragraph) and cannot abide such people. There are several problems with this action.
First, this is a reaction to a series of events, not any kind of moral principle. Unti the recent acts of lawlessness, they were, apparently, perfectly content to have all four of these people here in town.
Second, this action is just as lawless as anything that had already been done in town.
Third, there is no causality between the thefts, stealing, or death and these four people.
Finally, the decision is made by a "secret committee." This kind of anonymity allows people to do all kinds of things without being held accountable.
To add to the hypocrisy of the "Christian" act of ridding the town of these "undesirables," the town sends them off completely unequipped and unprovisioned for a winter in the mountains.
In short, forcing these outcasts to leave Poker Flat may make the town feel safer, which is the reason they gave for expelling them; however, there is no demonstrable evidence that this will happen (except, we learn later, in the case of the drunkard who probably was responsible for the thefts). In fact, we have evidence, as the story progresses, that three of these people are willing to sacrifice for others and have kind and generous hearts, despite their professions.