Racism is tied to power balance.
While I probably would avoid making fun of rednecks, I don’t think it is quite the same as making fun of jews, blacks, hispanics, gays etc. Rednecks don’t experience institutionalized racism. You will not be treated worse by cops and authorities for being a redneck. You will not be ignored by politicians. Rednecks are not marginalized in society even if intelectuals may make fun of them. People will even proudly describe themselves as hick or redneck. Btw this is my impression, feel free to correct me ;-)
That is quite different from the British chav for instance, which I find more derrogatory. Nobody ever calls themselves a chav to my knowledge. It is worse in Britain I think because Britain is a class society and mocking chavs is a partially a way of mocking the poor. People who may be described as chavs are treated more poorly by society. Sometimes snobbish conservatives will describe these people as feral. I don’t think American way of talking about rednecks is cruel in the same way, because I think many Americans themselves partially identify as red necks. It kind of goes hand in hand with the rugged individual idea. I don’t think any British person would ever want to be associated with being chav.