In fairness, speaking as someone from Georgia, you run into a lot of this within the south. I've lived here my entire life, and generally speak with a fairly neutral, midwestern accent, and I'd say that it's extremely common within the roughly 35 and under demographic around here.
Not commenting on whether it's fair or not, but because there is such a stigma around southern accent = stupid, many southerners, especially younger ones, make a concerted effort not to pick up the accent. Generally, the younger and better educated a southerner is, the less likely they are to sound like a southerner. That's not because the accent makes someone stupid, but because there is an awareness that it has that perception, so people avoid it.
And, I mean, I'll still fall into it in less formal settings or when I'm cranking up the charm, but in a business environment it gets switched off.
If you work at a large Silicon Valley company, there's always that one meeting where someone at the table, while obviously smart, speaks such an incomprehensible version of English, that whenever suggestions from their end are vocalized, everyone looks at one another with silent "did you get that?", nods politely and then moves on.
In Silicon Valley there are so many people from all over the USA, and from other countries, that this type of bigotry is less important. I can't promise it will entirely not be an issue, but I doubt it would be a big deal.