A lot of history and sectarian bickering here. First, Henry VIII outlawed the RC Church and created his own. All other churches were disenfranchised. He ordered that the established church (his own creation) keep B/M/D rcds.
The Church of England and Church of Ireland began to comply in the 17th century. There was no standard format, or list of things that should be recorded. The established churches began recording in mid 17th century. Catholics, especially priests, were hounded or murdered and dared not keep records of parishoners lest criminal charges be brought.
On the Protestant side, the Anglican church splintered first to Presbyterians in Scotland, then Methodists, followed by Quakers, Baptists, and fractures in the Presbyterian church. When in firm control, the established church (Church of England and Ireland) persecuted everyone. However, when the Catholic Irish rebelled, it deigned to beg help from the other protestants. Together, they subdued the Gaelic Irish. Only the established church was required to keep rcds. It did so, but grudgingly.
By the late 17th century, the penal laws against the catholics began to ease, and Catholic churches began keeping B/M/D records. Being better organized than the protestants, they developed and employed standard formats and collected required information.
By 1829, Irish Catholics were reinfranchised and allowed to vote (but not to hold elective office). In 1846, all protestants were required to register B/M/D events with the civil government. In 1864 Catholics were also forced to adopt civil registration.
Most of the civil records were collected from the hinterlands and put into a huge government building in Dublin. In 1922 during the Irish civil war, explosives stored there by the IRA blew up - destroying 1,000 yrs of recorded Irish history and most of the civil records. This is known as the Four-Courts Fire.
What rcds remained were the parish registers in the country, and some of the duplicated civil records.
Sorry to be so long-winded.
Nearly ALL of the remaining church parish registers have been collected by the Irish Family History Foundation and are in the process of being transcribed into digital format. Few, if any of the parish churches still have the old rcds.