How is them having mental health problems an argument for NOT giving them money? They didn't get the necessary health care they needed, so fuck them? Personally, I've never had a homeless person be overtly aggressive towards me, even if I usually look (not stare) at them as I pass them by. Edit: I'm not implying that you're staring at them.
My rule has now become that if they don't ask me for money, I will give a bit. If they only day it as I'm passing by, I may still give some, but I've decided that I will not support people who walk up to you and ask. I find it to be scoring and disruptive. To be honest, I haven't completely gotten around to following that rule every time, though. It's hard to follow a middle ground like this! It was easy back when I never gave money, then I would just automatically say no. Now I have to make a adopt of the moment value judgement, and it can be difficult to say no to someone who's down and out. I agree with this woman that they are people, and I will consider them as such. They probably don't enjoy panhandling. It's something you do when you're desperate. It doesn't cost me much to give a bit, and it makes a big difference to them.