In the book "The Irish (and Other Foreigners)" Shane Hegarty argues that the Irish are not Celtic

According to his arguament, the archaeological evidence shows Irish artifacts are not similar to Gaulish artifacts, or Hallstatt culture artifacts. In fact, he claims Ireland is actually comparatively less Celtic than most western European countries, in its artifacts. He also said there is no genetic evidence of the Irish being Celtic.

Hegarty claims the Irish are not Celtic, but does not suggest another greater racial/linguistic group to classify the Irish. If we are not Celtic, then what are we? In what way are we related to the Scottish linguistically (If we dont have a shared Celtic heritage than why are we similar?)

It must also be said that the paper that Hegarty writes for (Irish Times) does have a left liberal bias, perhaps his conclusions are motivated by multicultural ideology.

I am agnostic on the issue now, but I understand that the mainstream belief is that the Irish are Celtic. What does r/AskHistorians think?