YABU. Unless you decide that any form of subjective classification of groups of people is wrong, then why shouldn't 'chav' and 'common' be used?
Social groups have always been classified in one way or another. Think of yuppies, green-welly brigade, hooray-Henries, middle-class Ocado shoppers, Boden mummies, Notting Hill types etc. I don't see you up in arms about those kind of labels.
Chav and common are used in conversation and people will understand what they are in reference to. Generally, IMO, someone who is chavvy lacks taste, class and possibly education. It's not really anything to do with income. Chav tends to describe someone whose pride and joy is an enormous plasma screen television that takes up the entire wall of a room.
Conversely, 'old money' describes families who own an ancient television, an old AGA and have a drawing room.
Yes, these things are subjective labelling but so what?