The Irish constitution includes a Preamble that is explicitly Roman Catholic in tone and content, referring to 'Divine Lord, Jesus Christ' but more controversially, speaking 'In the Name of the Most Holy Trinity':

"In the Name of the Most Holy Trinity, from Whom is all authority and to Whom, as our final end, all actions both of men and States must be referred, We, the people of Éire, Humbly acknowledging all our obligations to our Divine Lord, Jesus Christ, Who sustained our fathers through centuries of trial, Gratefully remembering their heroic and unremitting struggle to regain the rightful independence of our Nation, And seeking to promote the common good, with due observance of Prudence, Justice and Charity, so that the dignity and freedom of the individual may be assured, true social order attained, the unity of our country restored, and concord established with other nations, Do hereby adopt, enact, and give to ourselves this Constitution."

The link between Catholicism and the Irish state has ensured that the Catholic Church has a central role in the Irish State, despite the 1972 repeal of Article 44, section 2, of the 1937 Irish Constitution, Bunreacht na hEireann, in which "The State recognizes the special position of the Holy Catholic Apostolic and Roman Church as the guardian of the Faith professed by the great majority of its citizens."

That pretty much made Ireland a Catholic state according to any definitions I've ever read. There has been some waffling about it, saying it wasn't enshrined as an official state religion in the constitution. But damn close enough, eh? The damning effects of Catholic repression were felt all over the country from the end of the famine onwards. The constitution merely enshrined the church's position, even after Article 44 was repealed, and the country has just barely begun to recover from it.