The mobs from the 'gimme people' will be the first to perish. They will plunder their own first out of desperation. By the time they run out of plunder and they hit the inner suburbs for those neigborhoods the word will be out and won't end well for the zombies..
It's the people who live in big cities with large populations of gibsmedats who would be in severe trouble. However, if they get to the more conservative (and armed) suburbs, the mobs again will be in big trouble. But that's also assuming there will be a complete breakdown of the authorities.
In the end, I doubt even with a major power breakdown, that mobs will be able to get too far. Even with the major power breakdown, most whites (at least in conservative areas) would band together to help each other and shoot savages of whatever color. I do not see a case where it's every citizen for him or herself.
saving yourself from this will be the first priority...