The whole Celtic thing seems to have followed the success of Enya’s ethereal (or woozy) singing, and, somewhat later, Michael Flatley’s convincing people that if one person doing step dancing is good, a battalion must be better. The word “Celtic” has been a big moneymaker ever since, especially for PBS, which trots out someone like Loreena McKennitt or the gawdawful Celtic Thunder (not to be confused with an earlier group of the same name, which was merely bland) for fundraisers.
Before that, there was a pretty good audience for Irish and Scottish folk music, as performed by The Chieftains (Irish), Planxty (Irish), The Bothy Band (Irish), The Boys of the Lough (Shetland Islands), The Oyster Band (English), Silly Wizard (Scottish) and many others. I personally love that stuff, so I might think it’s more popular than it is. There was also, and still is, Breton folk music, which is all but overlooked in the US, but has some fine performers, such as harpist Alan Stivell and guitarist Dan Ar Bras. And, of course, the punkoid offerings of The Pogues, Dropkick Murpheys, and the like.
Before that there were acts like The Clancy Brothers (usually with Tommy Makem), which had some popularity, and which later morphed into the duo of Tommy Makem and Liam Clancy, who are mainly remembered for their definitive version of “The Band Played Waltzing Matilda.”
Before that, I can’t think of much of anything except Maureen O’Hara pounding out old chestnuts like “When Irish Eyes Are Smiling” and “My Wild Irish Rose,” both American songs (see Chauncey Olcott). And there’s always been a market for Irish tenors, the greatest of which was probably John McCormack, who did the same songs earlier in the century.
I have no idea how the popularity of all the above compares among countries. America has more people of Irish extraction than anywhere else, including Ireland, so it’s the motherlode. I’d imagine there’s a fair market in Canada and Australia as well. Scottish Gaelic music apparently doesn’t sell too much, which is a shame, because singers like Julie Fowlis are wonderful.