I'm hypocritical and somewhat ambiguous on this question, as I'll explain later on. I think on the whole that people shouldn't change their accents from song to song. And I'm especially doubtful of Joe's proffered strategy of changing the accent in which one sings according to who is in the audience! You're likely to throw yourself off when you try to change your usual way of doing the song- and anyway, the native might be in the audience anywhere.

Poor imitations of an accent are very irritating to listeners who know the accent well. (Granted, the fine points of an accent are more obvious when speaking than when singing.) And how specific should the accent be? There isn't ONE Irish accent, ONE English accent, ONE American accent, etc. I think some people writing in this thread are confusing accent with using dialect words or different pronunciation of specific words. Though I admit that Scottish dialect can be so distinctive that it seems to cry out for a Scottish accent. I prefer to sing, for example, "Fareweel tae Tarwathie" to "Farewell to Tarwathie", and I do use some sort of Scottish accent - but I'm self-conscious about this and don't usually sing my Scottish repetoire in public! For one thing, I don't always know which dialect pronunciation is appropriate to an individual song. Recently in Skye, I was sitting with two men who were discussing a third man known as "Mouse". Although they were both talking together about the same man, the speaker from Kirkaldy, Fife consistently pronounced the name to rhyme with "house" and the speaker from Aberdeen pronounced it to rhyme with "Loose" - with no implication that "Mouse" resembled an elk!

I've had a few experiences of being distracted by what I felt were poor American accents by Irish actors or poor Ulster accents by Scottish and English accents. Nancy Griffith doesn't use an ersatz accent when she sings English language Irish songs, and she sings them well. Lots of Irish singers sing English songs (songs which they got directly from English sources rather than ones that have been well absorbed into Irish tradition) without altering their accents. Even if an accent is well done, the listener may feel the singer is being phoney. I remember feeling let down when I first learned that Ewan MacColl was a Brummie (I suppose he faithfully imitated his parents' accent?).

My ambiguity: I can accept what others in this thread have said about there being no overall prescription, that it depends on the nature and regional distinctiveness of the particular song and of the knowledge and skill of the individual singer. What bothers me most is people making unintelligent, unthinking choices to adopt an accent other than their own. After the Furey Brothers popularised "Willy McBride" (No Man's Land, The Green Fields of France), I heard pub entertainers in Derry singing the song with a Dublin accent copied from the Fureys. this struck me as absurd. The song was written by a Scotsman who has settled in Australia. The 'action' takes place in France and the singer could be of any nationality that had individuals fighting there in the first world war. A Derry accent would be at least as appropriate as a Dublin accent!
Well, I'm NOT ambiguous about the above example, but I am about this one. I'm a bit shy about mentioning it as Virginia Blankenhorn and her husband are sometime Mudcat contributors. But then,it could be good if Virginia responds to this letter. Virginia is American and she recorded an album in Irish-language in which she sounds to me like a native of Conamara. Okay, I'm envious, I wish I could sound just like I was from, for example, Rann na Feirste, when I speak Irish. But I felt that Virginia's singing was absolutely imitative, not expressive of herself. I mentioned my reaction to a native Irish speaker, Hugh Hudaí Og of Gaoth Dobhair, Co Donegal. He suggested to me that as a learner, rather than native speaker, Virginia had to take extra pains to represent the tradition faithfully. That makes sense to me. As a native English speaker, I feel much more free to alter English-language songs (even from different cultural backgrounds), and to sing them as I wish to (including occasional changing in phrasing, intonation, vocabulary), than I do to 'play' with Irish-language songs. If a singer pronounces a given Irish-language word differently than I would in speech, I would probably choose to follow the example of the singer in case changing it seemed inconsistent within the song - I wouldn't often have the confidence to make my own judgement on the matter.

About two years ago, I heard two interviews with Virginia Blankenhorn on Raidio na Gaeltachta. On the old recorded interview, she sounded like a native speaker from somewhere in Conamara. Since then, she had lived in Northern Ireland, in Scotland and moved back to the US. In the interview over the phone, Virginia's accent and vocabulary were more eclectic. She was equally fluent in both interviews, but arguably more 'correct' in the first and more authentic in the latter. Which example would I rather emulate?

My hypocrisy: My accent does vary with the songs I sing. I started listening to recorded folk song (mostly in English) from various ethnic and national origins when I was only 10 years old. My natural tendency was to imitate the accent of the singer, and a lot of my early inclination has stayed with me - especially when I am singing songs I learned in childhood and adolescence. Also, I have travelled quite a bit and I've lived in different places (mostly New York state, US and Derry city, N Ireland) and my everyday accent is a hybrid.