The Medieval Kingdom of England ruled over a fluctuating amount of Ireland, but English influence was weakest in Ulster (basically the part that became Northern Ireland). Ulster was the last part of Ireland to be subjugated by England, and James I secured the area by moving in large numbers of Scots Protestants, with effects that are still with us.
Its not clear why the Tudors were so interested in strengthening their hold over Ireland, but it may have been the possibility of the Spanish using it as a base. So one effect of England not going Protestant would be no Spanish threat -they were allied with the Habsburgs against France, and another would be no religious split with the Irish in the South. They just don't bother with Ulster, which eventually develops into a small kingdom.