It takes a lot of effort to unlearn an accent, but it's not terribly hard to learn a fake one to speak in different contexts. My mom does this. Her work accent is usually not very southern, unless she's exclusively around other southerners with accents, but even then her "public southern" accent is nothing like her accent with our family in appalachia. I'm glad my resting accent is relatively neutral. Even in the south, having a thick accent can make you a bully magnet.