No, it's mainstream. See, for instance:
The researchers did see distinct genetic groups within those regions but those groups were quite different from each other, according to Prof Donnelly.
"Although people from Cornwall have a Celtic heritage, genetically they are much, much more similar to the people elsewhere in England than they are to the Welsh for example," said Prof Donnelly.
"People in South Wales are also quite different genetically to people in north Wales, who are both different in turn to the Scots. We did not find a single genetic group corresponding to the Celtic traditions in the western fringes of Britain."
The finding is the first genetic evidence to confirm what some archaeologists have long been arguing: that Celts represent a tradition or culture rather than a genetic or racial grouping.
https://www.bbc.co.uk/news/science-environment-31905764Or:
The Irish also cherish another origin story, of the Celtic roots they are said to share with the Scots and Welsh. In the Celtic Revival of the 19th and 20th centuries, writers such as William Butler Yeats drew from stories in the Book of Invasions and medieval texts. Those writings described a migration of Gaels, or groups of Celts from the mainland who clung to their identity in the face of later waves of Roman, Germanic, and Nordic peoples.
But try as they might, researchers so far haven’t found anyone, living or dead, with a distinct Celtic genome. The ancient Celts got their name from Greeks who used “Celt” as a label for barbarian outsiders—the diverse Celtic-speaking tribes who, starting in the late Bronze Age, occupied territory from Portugal to Turkey. “It’s a hard question who the Celts are,” says population geneticist Stephan Schiffels of the Max Planck Institute for the Science of Human History in Jena, Germany.
Bodmer’s team traced the ancestry of 2039 people whose families have lived in the same parts of Scotland, Northern Ireland, and Wales since the 19th century. These people form at least nine genetic and geographic clusters, showing that after their ancestors arrived in those regions, they put down roots and married their neighbors. But the clusters themselves are of diverse origin, with close ties to people now in Germany, Belgium, and France. “‘Celtic’ is a cultural definition,” Bodmer says. “It has nothing to do with hordes of people coming from somewhere else and replacing people.”
https://www.sciencemag.org/news/2017/05/theres-no-such-thing-pure-european-or-anyone-elseIt's notable that the Greeks and Romans did not use Keltoi or Galli to refer to anyone in the British Isles - those were used for people on the continent. The Hiberni and Britanni, or Albiones, were the names for those of the islands.
https://books.google.co.uk/books?id=f899xH_quaMC&pg=PA846
For a long time the myth of Irish history has been that the Irish are Celts. Many people still refer to Irish, Scottish, and Welsh as Celtic culture. The assumption has been that they were Celts who migrated from central Europe around 500BCE.
Keltoi was the name given by the Ancient Greeks to a 'barbaric' (in their eyes) people who lived to the north of them in central Europe. While early Irish art shows some similarities of style to central European art of the Keltoi, historians have also recognized many significant differences between the two cultures.
Recent research into Irish DNA at the beginning of the twenty-first century suggests that the early inhabitants of Ireland were not directly descended from the Keltoi of central Europe. Genome sequencing performed on remains of early settlers in Ireland by researchers at Trinity University in Dublin and Queens University has revealed at least two waves of migration to the island in past millennia. Analysis of the remains of a 5,200 year-old Irish farmer suggested that the population of Ireland at that time was closely genetically related to the modern-day populations of southern Europe, especially Spain and Sardinia. Her ancestors, however, originally migrated from the Middle East, the cradle of agriculture.
Meanwhile, the research team also examined the remains of three 4,000 year-old men from the Bronze Age and revealed that another wave of migration to Ireland had taken place, this time from the edges of Eastern Europe. One third of their ancestry came from the Steppe region of Russia and Ukraine, so their ancestors must have gradually spread west across Europe. These remains, found on Rathlin Island also shared a close genetic affinity with the Scottish, Welsh, and modern Irish, unlike the earlier farmer. This suggests that many people living in Ireland today have genetic links to people who were living on the island at least 4,000 years ago.
https://owlcation.com/stem/Irish-Blood-Genetic-Identity
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