But not doing what you think the cops want you to do, i.e., tearing stuff up in your own neighborhood, might garner more sympathy.
What if, once in the neighborhoods, the protesters simply sat down and refused to move? No violent motions. Just sitting there, silent as the dead?
They would route traffic around them and the news media would get bored and leave.
Then the police would likely start rounding people up as gently as possible.

Food Stamp abuse and fraud comprise such a small minority of program users that it's just another red herring used by cultural conservatives to create scapegoats and draw attention away from far more endemic and systematic abuse of federal funds by people with real power and influence. Most Food Stamp cheats and abusers are caught and properly punished for breaking the rules and the law.
Buying shrimp cocktail or an expensive pizza with Food Stamps should never be a violation of those rules and laws.
+1