Perhaps the author misdirects in the opening (I hope so), but they seem to be caught in the reductionist culture=identity trope that much my home country of America suffers from. Examples here include absurdisms like "Obama isn't black enough" as if a black man isn't black if he doesn't act a certain way.
Many cultures are built in opposition to other cultures, yes, and while that is true, the entire of culture is that it's made up of the people within it. When that starts to change, it just changes, it doesn't go away. In my life America went from being known for it's light lagers, now it is know for over hopping all our beers. We went from Safeway to Trader Joe's being the dominate grocery chances. Is America not America? No! Is California more Californian? No!
Culture is the culture that the people in the culture choose to celebrate. There are no True Scotsmans, only Scotsmans, who occasionally disagree.
Ireland is the people in it. If they change their religion, and their national sport and drink, then they will be a different Ireland than they were, but they will still be Ireland so long as people identify as Irish.