You shouldn't have to be ashamed of how you sound or where you're from. I do massively agree with you regarding people thinking southerners are stupid bigots. The way to fix that is to show them you're not, and make a strong point of showing it.
It reminds me of a trip I recently took to Belfast. The day I was there, a car bomb from the IRA killed a police officer. A cabbie asked me if I supported Donald Trump and told he we was surprised I didn't. He told me all Americans supported Trump. So I asked him if he was an IRA thug/terrorist, to which he naturally said no. So rhetorically, I asked how he was from northern ireland and not IRA. When he explained what was obvious, I said EXACTLY, this is much like people who support trump in America. The vocal minority often drown out the majority. Blindly categorizing someone in $group is bigotry plain and simple. Just because it comes from an educated person in tech doesn't make it any less so. Perhaps point out this hypocrisy.