For those who want to do the calculations manually themselves you can use the CSO map itself:
Select an LGA and Select 'explore all themes'.
'Migration Ethnicity & Religion' is where this data comes under. Tables are easier for calculations (it presents default as a chart).
'Usually resident population by ethnic or cultural background' is where you`ll find what you need.
Direct data link:
Screenshot: This is what a 91.4% Ethnic Irish (White Irish + White Irish Traveller) area looks like .
Areas with higher rates of non Ethnic Irish correlate with more A) poor english (defined as those who do not speak english well or at all) and B) More 'Not Stated' for Ethnicity.