Man youre asking a question that would take a book to answer properly. Actually Id recommend Locating Folklore: Tradition, Modernity, Identity by Diarmuid O Giollain for a proper answer.

Traditional Irish Culture is the indigenous culture of the island. Say in pre history, the Indigenous culture would have been subaltern to the celtic cultures that ruled here by being a medium of social mobility. The low ranking deise tribes are an example of the indigenous separate from the celtic for a while before we blended together the greater indigenous adapting the best of the lesser number of celtic peopels and we became the Gael. Today we have our independance but our culture again is not a culture of social mobility, our language is a minority language and our culture contradicts capitalism. So to high culture in Ireland is a blend of those socially mobile cultures today like The French, the German and The American.

Traditional culture is just the native culture. If how it could be perceived to retain beliefs is an issue I recommend looking at the anthropological definitions for the social movement of 'Modernity' and the preceding 'Traditional' societies. Those are not science and technology and anti science and technology respectively they are just academic definitions of two popular if contrasting forms of societies in our world.