This is pretty good episode, mostly due to Sisko and Bashir's "coming of age." However, I think it truly misses the mark with "the message."
The Sanctuary Districts aren't examples of what happens when people at large stop caring, it's what happens when governments stop caring. What we have here is a situation where the government has forcibly relocated people it deems "undesirable" into special areas that are separated from the rest of the public. It then forces those people to remain there and violently reacts when they try to change their lives. Does that excuse the fact that the general public seems oblivious? No. However, I would say it shows that people are under the impression of "well, the government is taking care of the situation, so why should I bother with it." Whenever the government takes over something like this, you get the extreme overreaction of storm the place with guns blazing, and that isn't justified either. Private individuals and groups need to step up and deal with the situation in a humane way - something governments, IMHO, aren't capable of doing.
We also have a situation where the government is using rationing to control the public - just like big governments tend to do. When Sisko and Bashir are first caught, they're asked to produce their "U.H.C. cards" (Universal Health Care cards maybe?). When they can't do that, they're immediately assumed to be vagrants and carted off to the District by men who work directly for the government. And yet, amazingly, the episode never makes mention of the fact that if it wasn't for these government programs the problems wouldn't exist in the first place. No, instead it's the fault of the general public for "not caring."
You get the distinct impression that the episode's ultimate message is that what is needed is an even larger government to come in and fix the problems even though it was the government that caused them in the first place. Intervention wouldn't solve the problem of intervention.
Of course, all that ignores the problem of B.C. being a cold-blooded killer who gets a pass just because he's homeless.
Sometimes the show delves into libertarian ideas like this (Shakaar
being another example), but often doesn't follow through with them.