What’s the difference between “come recommended” and “be recommended”?

… But their main business is in parts and refurbishing, and the old man, Deforges, doesn’t like to sell a used piano to someone who hasn’t come recommended. He says it’s more trouble than it’s worth and he’s got plenty of customers for the pianos that come his way. (The Piano Shop on the Left Bank by Thad Carhart)

I think the rough meanings would be the same if the sentence used “who hasn’t been recommended” instead of “who hasn’t come recommended,” but what’s the difference between them?

There's no real difference in meaning - it's largely style.

Having said that, to come recommended is at the very least "dated". Here's a chart showing how usage has fallen off since the first half of C19. Most people today would say "...someone who hasn’t been recommended." It's also more "gentrified" (perhaps just because dated expressions often seem more refined), so it better suits OP's context of personal recommendation within "genteel" society.

Note that recommended has two distinct meanings, as covered by this earlier question. In OP's context, if the customer were to be recommended, that could either mean that he was advised go to Deforges because that was thought to be the best place to buy a piano, or that the customer was thought to be good enough for Deforges to deal with. There is no such ambiguity if the customer comes recommended - it's always the latter meaning.