(I'm a Dubliner and I would accept the label.)
I think that Celt is generally confused with Briton (Preton/Pretanike - Pytheas) thanks to some fanciful thinking over the last few hundred years. You might also notice: Britany - a region of modern France. The "indigenous" Britons were duffed up by various invaders. The Scots migrated from Ireland and the Picts went the other way etc etc. Angles and Saxons, Norwegians and Danes farted around at various times (we had a King Knut/Canute famous for talking to the sea - he didn't really - he was emphasising how the sea is unstoppable (or was he!)
These isles off of the left hand side of mainland Europe have a pretty complicated history but perhaps not as complicated as say what we now know as France, Germany, Italy and co.
The Celt thing is a bit ambiguous at best ...