It's natural to be frustrated and annoyed by homelessness at times, but surely it's easy to also feel compassion for these people, too, no?
That being said, I don't have much compassion for people who harass me incessantly for money and scream obscenities at me when I won't give them any; who pull weapons on my friends and mug them at knife point in broad daylight; who urinate and shit in public without even making an attempt to seek privacy; who are violently disruptive just to do it; who shoot up drugs on the street and make no attempt to seek treatment or be part of society; who get on public transport and start screaming about their schizophrenia-induced religious nonsense; etc.
These individuals certainly show no respect or compassion towards me or to people I know who have been assaulted by them. Why is it my responsibility to deal with them as a private citizen when many don't seem to even want to be helped and when the government who I pay taxes to in part to ensure my public safety doesn't seem to care either?
Then there's the issue of many mental disorders strongly affecting executive functioning, which is required to keep appointments with their healthcare provider. Even people in the most stable of circumstances miss appointments; now think how difficult that would be when you don't know where you'll be sleeping that night (plus aforementioned mental health issues).
All of these issues compound on one another. I have nothing but sympathy for people experiencing homelessness, and nothing will change that.
They were homeless, and mentally ill, because they chose to use powerful, mind-altering drugs that fucked up their brains. They chose to keep using those drugs.
I have absolutely no sympathy for drug addicts. Using drugs is a choice. The fact that it has serious consequences does not engender sympathy. If anything, the fact that people know drugs will fuck them up and still use them anyway makes me less sympathetic to drug addicts.
I have great sympathy for the homeless who are merely down on their luck. You can identify them pretty easily. They're the ones that aren't drunk or high, and they're usually in the shelters at night because they'd rather have a hot shower and a hot meal than spend a night on the street with the addicts.
And yes, every single one of them absolutely feels contempt for the homeless who choose the streets over shelter just so they can stay high. I worked with enough social workers when I was a public defender to have a better grasp of their views on the homeless than you do.