I choose to make donations to charitable foundations instead of cash to street panhandlers.

But when someone asks me for money on the street, I almost always respond to them by saying "Sorry" or similar. I've always felt it rude to just walk by ignoring their presence. And probably over 95% of the time the person answers back something like "ok, have a great weekend" or "Thanks anyway".

That said, I think many people that walk past without making eye contact do so not because they think the person begging is inferior, but likely because they're hiding in their own shame.

I've seen similar behavior on crowded subways, where able-bodied people avert eye contact with the pregnant lady or senior citizen who is standing, wanting both to keep their seat but hoping someone else gives up their own seat.