Vikings & Normans were small minorities (<1-3% of Irish population) so they were absorbed culturally & genetically into the Irish population. The Plantations—15% of population over 140 years, remain a problem (>10% so no need to assimilate). Ireland is currently 23% foreign born.
I think the point is that we are all descendants of immigrants. The Gaels displaced the previous inhabitants (Tuatha De Danann ?). Then came Vikings, Normans, English, Scots, and more recently Italians, Poles, eastern Europeans, Asians and Africans.