It is very, very rare to be Gaelic with no Nordic. There are some left, apparently the Healy-Raes (political family from Kerry in the south west of Ireland) are pure Gael according to a DNA test one of them did on TV. But we had a couple of big waves of Nordic influx and they tended to adapt and mix with the locals, and were obviously a lot better looking than the locals, so nord/gael is essentially the standard Irish ethnic background these days.