Like I said, it's complicated. For instance the BBC is numerically over-represented with Scottish radio and TV presenters. This is largely due to the perception that the Scottish accent is 'class-less'. It isn't of course but is more acceptable to the English ear than differing regional English, hence Shaw's quote about an Englishman only needing to open his mouth to make other Englishmen despise him. Whether this is institutional racism against the Scots or positive discrimination on their behalf is difficult to say.

Some people can get away with singing in different voices better than others. If your Trinidadian is impeccable you might pull it off because you're removed from problematic historical debate, being ethnically Chinese, but if you get it wrong you might be seen as an amusing novelty, like Margarita Pracatan the Cuban who featured on the Clive James show. That might be a highly employable novelty, but not in control of the way you are popularly perceived.