This isn't my area of expertise but those numbers do seem unbelievable at first glance. The book referenced in the Wikipedia article stresses the facts that its figures are tentative, and "should be taken with a pinch of caution and pound of scepticism".^(1) Having looked at some more recent work, it appears that the death rate was closer to 15-20%. (Edited to add that this % is still huge!)

Micheál Ó Siochrú is an expert on the 1641 Rebellion, Cromwell, and Ireland in the 17th century but I unfortunately don't have access to his 2009 book God’s Executioner: Oliver Cromwell and the conquest of Ireland, which is likely the best recent work on the subject. Elsewhere though, Ó Siochrú states that:

Between 1649 and 1653 Ireland suffered a ‘demographic catastrophe’, with mortality in the region of 20 per cent due to the continued fighting, alongside widespread starvation and disease^(2)

He cites Pádraig Lenihan (1997) for this statistic, who himself states that the countrywide mortality rate in Ireland was 15-20% in the period 1649-53.^(3) Owing to the time period, there are issues with accurate statistics (including knowing what Ireland's total population was, which would impact the mortality rate) but Lenihan's work is extremely detailed and I would accept his findings as being fairly accurate.

It's also important to note the role that disease played: plague spread throughout Ireland in 1649-1652, possibly the bubonic plague, typhus, or spotted fever. Prior to this, Ireland had not experienced a major epidemic for 50 years or so, and Lenihan believes that this means the popuation lacked natural immunity and the virulence of the infection was therefore amplified.^(4)

Deaths in this period weren't just the result of intentional killings so the word 'genocide' isn't entirely appropriate (without getting into Cromwell's actual massacres in Drogheda and Wexford); the associated effects of war (disease spread by migration and armies and famine) played a significant part. The 41% estimate seems to be inaccurate and/or outdated, but mortality in Ireland was still considerably higher than that in Scotland and England.

Thanks for bringing this up!

References:

^(1) Charles Carlton, Going to the Wars: The Experience of the British Civil Wars 1638-1651 (1994), pp. 213-14.

^(2) Micheál Ó Siochrú, 'Atrocity, Codes of Conduct and the Irish in the British Civil Wars 1641-1653', Past & Present 195:1 (2007), pp. 55-86: 80.

^(3) Pádraig Lenihan, 'War and Population, 1649-52', Irish Economic and Social History 24 (1997), pp.1-21: 19-20.

^(4) Lenihan, pp. 10-11, 19.

(Edited almost immediately for typos)

I'm originally a specialist in nineteenth-century Ireland but have a strong secondary interest in the seventeenth-century. An initial comment on the question is to unpack the idea of an "English Civil War." That's now totally out of favour and the idea of a "Wars of the Three Kingdoms" is more accurate. The conflict began in the late 1630s with Scottish resistance to King Charles I's religious policies. It was exacerbated by a rebellion in Ireland in 1641. Charles' relationship with the English Parliament broke down into warfare by 1642, but to see the conflict as a merely an English civil war is inaccurate. There was an internal civil war in Scotland during the whole period as well, whilst the main body of the Scots government was allied to the English Parliament. This didn't last, and by the 1650s the English Commonwealth was at war with their former allies in Scotland. The Anglocentricity of the historiography is incredible, though. The 1650-51 campaign was a straightforward war between the English Commonwealth and the Kingdom of Scotland, then ruled by Charles II. Yet it's often called the "Third English Civil War," even though almost no English people fought on the Royalist side.

For Ireland, we also need to unpack the idea of "the English" killing almost half the population. From 1641 through the 1650s Ireland experienced an incredibly devastating multi-sided conflict. How do we define the combatants? It isn't just "the English" and "the Irish." Ultimately, there were Royalist forces loyal to Charles I as King of Ireland, and these armies had both English and Irish soldiers. There were English forces loyal to the English Parliament. Later on, the English New Model Army campaigned in Ireland during both the Commonwealth and Protectorate periods. The Scots had an army in Ulster in the early phases of the fighting, and there were Irish Confederate forces. However, these were internally divided between leaders considered to be "Old English" and "Old Irish," meaning, respectively, descendants of medieval English magnates and the pre-existing 'native' Irish. The Confederates were Catholic, however, including the Old English. There was a significant amount of changing sides as the wars progressed, not because of pure duplicity, but because war aims, alliances, and interests were constantly shifting in the multi-sided conflict.

Within all of this, any agrarian society that experiences over a decade of incessant warfare will suffer. These armies lived off the land, so food shortages and the disease that inevitably accompanied early-modern armies would have a substantial impact. Sieges could be devastating for the cities targeted. Lastly, and this is controversial, there is no question that civilians were targeted by the combatants, from the start. The wars began with a rebellion in 1641 of Catholics who proclaimed their loyalty to King Charles but sought to regain lands and station, and this rebellion did involve the mass-killing of Protestant settlers. However, Protestant forces killed Catholic civilians in reprisal, and the protestant press in England didn't publicise those atrocities in the way that Catholic treatment of protestants raced off their presses. Because of the notorious massacres, we look for civilian deaths in combat. They happened, without question, and the debates on what constituted the early-modern European 'laws of war' and appropriate action isn't something we need to get into here. But the length of conflict, the constantly shifting fronts of multiple armies trading territory, the fragility of foodstuffs before preservatives and canning, never mind refrigeration, and the ravages of plague and illness that followed armies has to be taken into account.

Overall, the picture is more profound tragedy than evil.

During the chaos of the English Civil War, Catholics in Ireland rose up to fight against Britain for a variety of reasons. Chief among these was the protection of Catholic rights. Parliament was rabidly anti-Catholic, so it was seen as an opportunity by the Irish to fight back against measures to restrict and oppress Catholicism. The 1641 rebels organized into the Confederation of Kilkenny, but this organization had different factions that eventually contributed to its demise.

The more moderate faction of the Confederation were made up of the Old English of Ireland. This was a group of English immigrants that had came to Ireland long prior. They were distinct from the Native Irish, but they were connected by their Catholicism, having left England before the English Reformation. They had the shared interest of protecting Catholic rights.

The most radical of the Confederates were led by Papal Nuncio Rinuccini, and they sought to completely remove Protestantism from the island. Starting in the early 1600s, the English Crown had taken up a program of completely pacifying Ulster, Ireland's most rebellious region. Wars and resistance to English rule proved too costly to maintain, and after Ulster's Earls were defeated in the 9 Years' War (1593-1603) the English Monarchy supported a plantation system to crush Irish resistance. The crown and London investors provided land grants to those willing to build fortifications and fund the settlement of English and Scottish Protestants that would farm the land. Native Irish were supposed to have been pushed from the land, but Protestant settlement did not occur in great enough numbers and the natives for the most part remained as laborers. The movement of Protestant English and Scottish settlers to Ulster and Catholic natives from Ulster would in theory Anglicize Ulster to keep it peaceful and profitable.

This population of Protestants were Rinuccini's target, and they made up a large portion of deaths in Ireland during the conflict. About of quarter of Irish Protestants may have been killed by the end of the Confederation, although this number is inflated by the high proportion of Protestant soldiers included in the tally. Protestant media in Britain played up and over-exaggerated atrocities, but they were based in truth. The Catholic uprising from 1641-1649 was terribly violent and filled with unjustifiable slaughter.

Splits between moderate and radical factions weakened the Confederation of Kilkenny overall. It made Ireland an easier target when Cromwell finally arrived in 1649. Cromwell's invasion was devastating. I won't touch too much on it, but the most well-known examples of this were the massacres at Drogheda and Wexford. Cromwell's invasion in conjunction with the policies put into place after reestablishing rule created his infamous reputation within Ireland to this day. Tens of thousands of Irishmen were sent into indentured servitude across the Atlantic, and massive portions of formerly Catholic-owned landed was granted to Protestant allies and elite.

During the English Civil War there was an incredibly violent revolution led by Irish Catholics followed up by an incredibly violent reconquest by Cromwell and the Commonwealth. In addition to actual fighting, war brought disruption of food supplies, famine, and plague. I can't assess the veracity of specific numbers, but it was indeed deadly.

Most of this information comes from Moody's The Course of Irish History as well as a few other sources I can try to find.