How do you deal with external problems you can’t solve around you? What is the moral thing to do here?
You don’t, you deal with your internal problems, like classism, ableism, and general ignorance of these people’s circumstances. Instead take the time to understand, learn empathy, show compassion and solidarity, instead of disdain. You don’t have to give people money you don’t have, but the least you can do is show them basic respect (no, homeless people aren’t all alcoholics or addicts, but many of those who do drink or use drugs do so to try and ease the deep distress of being homeless. And no, homeless people aren’t dangerous, those who create a society where they have to exist to keep people like you in line, are). (Edit to clarify: once you care about homeless people, rather than fear and/or look down at them, and understand the many reasons that lead to homelessness, you’d be equipped to actually tackle the systemic issues, but you can’t do that if you refuse to see them)
You are literally a blink of an eye away from being in their shoes, act like it.