From my limited point of view, I have noticed that some speakers with strong accents seem to be oblivious to the fact that they are hard to understand. They speak grammatically correct sentences and they sit on that knowledge seemingly thinking it's enough, that it's me who's stupid for not understanding what they said. The problem in those cases is that through their confidence, they try to speak too fast for their ability to clearly pronounce words and their syllables, which results in a long stream of garble to my ear.
English is my second language, French being my native tongue, and I do have an accent myself, but I try to speak individual words and syllables clearly. I still have an accent, maybe 'strong' but I'm pretty sure everybody can understand clearly the words I speak, or at least most of the time.
My wife is also learning English as a second language, Vietnamese being her mother tongue. Recently she's been improving a lot in her classes and begun to be overconfident in her ability to speak, trying to use contractions everywhere. Consequently, she's been having a harder time to communicate with others. My recommendation to her was to slow down and pay attention to say every word clearly before jumping into more artistic manipulations of the language. Surely it was frustrating to her, feeling she was moving back to a more primitive use of english. But she's also been improving her ability to be understood by other speakers.
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.
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.