I have a scouse accent, which commonly gets used in UK comedy as a byword for thuggishness, stupidity, and a propensity to steal things.
I don't get offended by it, I can generally find it funny because its a shorthand to express certain cultural and personal values. Anytime its done right, its making fun of the stereotypes attached to the accent, not anyone who happens to have the accent.
Now you could argue that its a lazy way of getting those things across, which is probably right, but taking offense at it seems kind of pointless.
The only way I'd be offended by it, is if i thought my accent was an important part of who I was. Which it isn't. Its just an unimportant quirk caused by unintentional circumstances of birth.
If anyone finds the accent funny because they truly believe anyone with that accent is one way or another, then thats their retarded problem.
As has been mentioned, on radio its difficult to try and put across impersonation, i.e. that you are representing opinions other than your own, without making changes to your voice.
and redneck seems to be the most commonly accepted signifier.