Evidently, it is ethically wrong for anyone to have money if they are Republican, and completely ethical to have money there if they are Democrat. At least, that's how the media sees it. John Kerry (SecDef) has a considerable amount of money in offshore accounts, as do many of Obama's cabinet appointees, and indeed Obama himself in his retirement account. This fact is not embarrassing because a Democrat can not be embarrassed by his wealth, former associations or KKK membership, or his sexual proclivities. Evidently, he also cannot be embarrassed by failing to take action when an ambassador is attacked. It's an odd world we live in, when shame is not experienced for a failure.
Romney was running for president and the stability of a Cayman Islands bank could both affect his policy judgement and be affected by his policy actions. Although with our government's structure that isn't a lot of power, it's enough to be ethically questionable. Also, holding offshore accounts demonstrates a willingness to avoid taxes through banks which aren't usually accessible by average citizens, which appears a bit elitist. Members of the president's cabinet with offshore accounts can experience the same conflicts of interest that the president could, but their executive power is generally less. So it's probably best to say that a cabinet pick with offshore accounts is less ethically questionable than a president would be, but both are still a bad idea. It's not the first time someone in the government has said "it's bad when he does it but OK when I do it."