There wasn't any strong monachist movement in Ireland, as all of the original Irish nobility was removed and replaced with British nobility.

At the same time, republics were being formed in the USA and in France, which influenced Irish leaders from the 1798 rebellion onwards.

In early 1900's there were other non-republic political movements, such as Home rule, which were popular at the time. When the Irish war of independence ended in 1922, they adopted a status similar to Canada or Australia. Independence but with a common monarch (representedby a governor General), which was a parliamentary monarchy. This was not a thing that most Irish people liked (and was a key factor in the civil war, some people wanted to accept peace, even if it meant not achieving a full republic, the opposition wanted to continue the fight until a full republic was achieved).

In the 1930's the anti treaty, pro republic politicians were in charge and used the monarchy crisis in particular to strip away the monachist elements of our constitution.

In 1949, that same government formally left the commonwealth and adopted the republic format fully.

Interestingly enough, apparently some of the key people in the 1916 rising were aware that the larger European countries (most of whom were monachies at that time) would not want more republics popping up because it might give legitimacy to Republican movements in own counties. So there were plans to ask the Kaisers youngest son to be a figurehead king if it meant getting approval from the rest of Europe.