There is an interesting article on Wikipedia (not always a valid historical source, admittedly, but nevertheless) concerning Ireland's history under the Tudor and Elizabethan regimes.
History of Ireland (1536-1691)The pre-Elizabethan Irish population is usually divided into the "Old (or Gaelic) Irish", and the Old English, or descendants of medieval Hiberno-Norman settlers. These groups were historically antagonistic, with English settled areas such as the Pale around Dublin, south Wexford, and other walled towns being fortified against the rural Gaelic clans. However, by the 17th century, the cultural divide between these groups, especially at elite social levels, was declining. For example most Old English lords not only spoke the Gaelic language, but extensively patronised Irish poetry and music. Intermarriage was also common. Moreover, in the wake of the Elizabethan conquest, the native population became defined by their shared religion, Roman Catholicism, in distinction to the new Protestant British settlers and the officially Protestant British government of Ireland.
It seems clear that Ireland pre-Henry VIII was a society divided on ethnic lines, with the ''Old English'', especially around the Pale, distinguishing themselves from the Gaelic Irish found elsewhere - particularly in relation to loyalty to the English monarch. With the advent of Protestant colonization, the Old English lost their privileges, but, for a time, remained loyal. However, by 1641, any hope of a reversion to the old order was gone and the Old English threw their lot in with the habitually rebellious Gaelic Irish (or converted to save their titles) and formed a new Irish identity predicated more on Catholicism than language or ethnic background as was hitherto the case. After the failure to confer the Graces in the 1620s and 30s, the Old English in the Pale decided the only recourse lay in rebellion, and the routing of the New English Protestant settlers to re-establish their old rights and influence. So, at least, it seems.
One may agree with or dispute the above, but I'd be interested in hearing more as regards when Catholicism and the concept of being Irish first became extensively interrelated.