I agree with the many who've said "whatever works".

However I'd never agree that songs "belong to" and should only be sung by people of the same ethnic background as the song. It is cross-cultural pollination which has given history its most memorable and greatest movements! Therefore to be opposed to such things is in my view very foolish.

Take the visual arts for example; it was the Saxons who introduced to the British isles the basic north european "ribbon work" which today is commonly missidentified as a "celtic" or Irish art-form because these days it is the manuscript illumination of the monks of the Celtic Church which we regard as the highest and greatest development of that art.

If we were limited to ascribing forms only to their originators, or their decendents, then this "Celtic" artform would suddenly become English! I can see no good reason why anyone shold be prohibited from singing an Irish song on the grounds of their being not-Irish!   

But what never works is a singer who has confused accent with dialect and tried to sing a dialect song in their own accent - which results in many dialect words being "mistranslated".

As an example (and of sight-spelling too) there's a Scots tune called "Fluers of the Forest" the title of which is cited in an Eric Bogle song. Singers who do not realise the quoted title is dialect, rather than Eric's accent, mis-sing it as "flowers of the forest" whereas the translation from Lalans to English is actually "floors of the forest".

So while I don't care if someone sings in their own accent rather than the accent of song's origin (heck, I'm a Planxty/Andy Irvine fan and he sings everything from everywhere in his own accent, to the extent that many folk think many American and English are actually Irish!), it does get under my skin when dialect words are not either left alone or mistranslated by the assumption they are mere variation in accent.