So I've been curious about this one. This is probably as much a question about the historiography as about the history itself.
The Anglo-Normans were the folks (largely Normans) who crossed over from Britain in 1169 and conquered large chunks of Ireland in the Medieval period. They spread things like stone castles and towns across the areas they ruled, before their control weakened in the 14th century (I've heard it connected with the Black Death) and "native" Irish lords reasserted control. The Anglo-Normans nevertheless remained a major political force until the Tudor period, at least.
So my question is: how long did they remain a distinct group?
Normans as Normans (and explicitly not Saxons) seem to have disappeared from England really within a couple of generations. Did a separate identity persist longer in Ireland? Do concepts such as "Anglo-Norman", or "Old English" have more to do with a modern (19th-20th century) nationalist reinterpretation of Irish history (meaning they are seen as something apart from the "native" Irish, even if they assimilated to being "more Irish than the Irish themselves")? Did they retain Norman French as a language? Or speak English dialects like the Yola and Fingal dialects? Does it even make sense to speak of Anglo-Normans as a group outside of aristocratic circles?
This is a question fraught with tension but I will try to answer it as best I can. In fact, I'll be presenting at the American Conference for Irish Studies in Boston this week!
After the first few centuries of Norman settlement in Ireland, they began to become "Gaelicized" and, as the saying goes, "more Irish than the Irish themselves." They began to integrate culturally, speak Irish (bilingually), and follow the norms of Gaelic lords -- e.g. patronize bards, harpists, etc. But they still clearly conceived of themselves as distinct from the Irish, evidenced by the Parliament of Ireland's continued exclusion of Gaelic Irish peoples in the late middle ages.
Things began to change around the Desmond Rebellions of the 15thC, the Reformation and the time of the Elizabethan conquest (reconquest?) of Ireland. "New English" settlers and officials, such as Edmund Spenser, began to argue that the "Old English" could not be trusted. That they had become Irish through "degeneration." (See: Nicholas Canny, Making Ireland British).
The Old English, however, did not see themselves as Irish at this time. They saw themselves as lawful, loyal subjects of the English monarchy, noble conquerors of the Kingdom of Ireland. Thus when the Gaelic lords Hugh O'Neill and Hugh O'Donnell led the Ulster Rebellion that became the Nine Years War (1594-1603), the Old English largely fought for the Crown and against the rebellion. (see: Hiram Morgan, Tyrone's Rebellion).
But after the Nine Years War, the accession of James I, the Flight of the Earls (1607), and the growing power of a New English and staunchly Protestant class in both Dublin and London, Old English Irish Catholics began to perceive that their interests as a group were not aligned with the Crown but with the Gaelic Irish and Rome. This is perhaps best represented by Geoffrey Keating, a man of Old English descent who wrote the famous Foras Feasa ar Éirinn ("The History of Ireland") in 1634 in which he articulates the quickly popularized and still persisting idea that the Irish are all Catholics in Ireland. He was, perhaps, the first to argue that the Old English and the Gaelic Irish were one people.
The Irish Rebellion of 1641 thus saw Old English and Gaelic Irish fight together. But, still, differences persisted. The Old English tended to remain royalists in the broader War of the Three Kingdoms while the Gaelic Irish tended to be pro-Rome and pro-independence. Nonetheless, both sides lost when Cromwell won. (Siochru, God's Executioner). Cromwell's hatred of Catholics and the militant Anti-Popery of the English and Scottish in the late 17thC and early 18thC totally collapsed the differences between the two from the perspective of the composite monarchy. This was even more clear and more resolute following the War of the Two Kings (1688-1691) in which the Catholics of Ireland again fought together but against lost. The result was the ousting of Catholic King James II in favor of Protestant King William of Orange. After this, the penal laws followed and excluded all Catholics (see: O Ciardha, Ireland and the Jacobite Cause & Morley, The popular mind in eighteenth-century Ireland).
From Keating's articulation of the Irish nation as Irish Catholics through the seventeenth and eighteenth centuries in which extreme anti-Catholic measures, if unequally and poorly enforced in the 18thC, brought the two populations together. Differences persisted, but certainly by Daniel O'Connor's time they were minor and subsumed under the ideal of a Catholic Irish nation.