I would call it maybe a tad of an exaggeration that the Black Death killed "far more" Normans^^1 than native Irish, but there was certainly a trend worth looking at.
To give a bit of background, the 14th century was a particularly awful time for Ireland (which is saying something) for Norman and Gael alike. The Normans had successfully conquered and occupied most of the island, but a consecutive series of crises (in tandem with London being far more occupied with affairs in France) resulted in the "Lordship of Ireland" as it was known, rapidly losing ground to the Gaelic Irish kings and lords who ceaselessly raided and besieged the porous borderlands between their own lands and those of the lordship. Then in 1315 Edward Bruce, brother of Robert Bruce, King of Scots, launched an invasion of Ireland with the support of the Irish rulers of Ulster to open a second front against England during the Scottish War of Independence. Bruce was declared King of Ireland (admittedly in a very nominal sense) and ravaged the country, particularly the more densely populated urban settlements and their surrounding hinterlands. While he was eventually defeated and killed in battle in 1318, large swaths of the country were in ruins. This was further worsened by a concurrent famine from 1315-17 (which affected all of Europe) but hit Ireland particularly hard (and in fact is what took the momentum out of Bruce's invasion). On top of that in 1333 political crises broke out when one of the most powerful Anglo-Norman lords, the Earl of Ulster, was assassinated, his vast lands being divided amongst his three sons and soon falling into civil war and large parts defecting from English control. So, on the eve of the Black Death arriving, the island was already reeling from devastating war, economic and agricultural exhaustion, and a highly chaotic political system plagued by endemic low-level conflict. It's good to keep all this is mind to contextualise the impact of the Black Death on Ireland.
The plague arrived in Ireland in 1348, starting in the eastern port town of Drogheda and spreading rapidly southwards from there, soon reaching the capital of Dublin and from there continued to hug the eastern shoreline. This general region of urban coastal settlement on the eastern shore was known as "The Pale", the region of Ireland under direct English control (in comparison to the more autonomous lordships elsewhere). To fit the surprisingly brief answer to your question in my overly long answer, the Black Death in general had a higher infection and mortality rate amongst the Anglo-Normans than the Gaelic Irish because the former resided primarily in dense, well connected urban settlements that facilitated the rapid spread of the disease, while the latter resided in far more dispersed, rural conditions that limited its spread. Contemporary accounts do notice this phenomenon, the English chronicler Geoffrey le Baker writing the disease "killed the English inhabitants there in great numbers, but the pure-blooded Irish, living in the mountains and high lands, it hardly touched". We have no definite numbers of how many people died, as other contemporary estimates provide numbers simply not possible, and any demographic projections would be little better than a random guess, although for the period in general some estimate the population of Dublin declined by 40%.
The Gaelic Irish were not spared, they too suffered greatly and the disease was remarkable in its ability to penetrate every strata of society and culture, but there is an agreed upon trend as to differences in mortality between the two major cultural groups, and the cause of said difference.
^1 The terms Hiberno-Norman or Anglo-Irish are the most common names to describe the descendants of the Norman conquerors of the 12th century that were born and lived in Ireland, absorbing some parts of the native culture. Anglo-Norman may be used in cases of no notable cultural exchange.
###Reading:
C. Downham, Medieval Ireland (Cambridge, 2017), Chapter 8 "Society AD 1100–1500: Plague and Famine".
M. Kelly, A History of the Black Death in Ireland (Tempus, 2001)
M. Kelly, The Great Dying: The Black Death in Dublin (Tempus, 2003).
M. Kelly, ‘Unheard-of Mortality…. The Black Death in Ireland’, in History Ireland, xi, iv (2001), pp 14-17.