Actors don't always achieve perfection either and everyone sounds a little different, doesn't really matter if you can pass.
A lot depends on the particular English/American dialect/region. Certainly many English/Scottish accents that would be seen as bad/easily dismissed. And many dialects in America that get the same reputation. Certainly some urban areas that have very distinct accents, some of which you may have heard of like Cockney. The acceptable accents you see in English media are usually from a few distinct areas of Scotland and Southern England. The famously made fun of one is the Chav, which is people that attend "public" school (private school pretty much everywhere else) and the high class universities like Cambridge. That is the high class British aristocrat, someone like Boris Johnson is an interesting example.
If you want a very interesting example, listen to Sandi Toksvig. She is Danish, but grew up in America, went to an English boarding school and adopted the accent of a famous black and white British actress.
What you see on American television and media is closer to Standard American English when actors aren't doing something regional on purpose. This is what broadcasters are taught in school, regardless of where they are from.
Ohio. Northern Indiana, Michigan, Illinois (Minus Chicago) are generally considered to be closest to this standard. East Coast and urban cities have distinct accents across America. Boston, New York, Chicago as examples. West Coast accents are also pretty noticeable, but because things like LA/Hollywood are where the US popular media comes from, a lot of that area also holds more closely to SAE. with greater differences in sentence structure rather than accent.
US also has the Southern (East Coast South) and Western accents (South West). These are your Louisiana/Deep South accents and are often the butt of jokes in US. Though there is also high class Southern which is more traditional among the wealthy in that area. Western accents go more towards your classic cowboy / farmer and it spreads through most regions of the US. If you make a living around livestock or farming pretty much anywhere in the mid-west, you will see this type of inflection and word choice.