The accent bit happens in the US too, to an extent. Depending on the accent you grew up with, you get different responses from people in professional or professional-adjacent settings if you forget to switch the knob back to the more homogenized vaguely Iowa-sounding GenAm accent. This covers a gamut of other accents - regional or not (NE, aave, southern, val, etc).
But it's not nearly as bad as RP in England from what I gather - for one, a pretty decent chunk of the population would normally grow up with a GenAm accent with no forcing, unlike in England where it's a pretty hyper local <5% of the native population.
Deference is given to your professional title, doctor, lawyer etc.
What nation on Earth doesn't have class issues?