Do you have a specific quote or passage you can provide that lays out his argument? I think I know what argument you are getting at but I also would not want it to be misrepresented.

The basic problem with this argument is that depending on how it is framed it is both obviously true and obviously false. For the past fifteen hundred odd years the great majority of people in "the west" (avoiding that particular argument for now) considered themselves followers of Christ, and that their worldview was shaped by the teachings of the Christian Bible and that they themselves were members of a community that was dedicated to following God's will. A poor farmer in the countryside of ninth century Italy, a noble woman in the court of Louis XIV, and factory foreman in Victorian London--all of these people (with rare exceptions) would have considered themselves to be followers of the teachings of Jesus. In that way, Christianity has certainly exerted a powerful influence on the morality and worldview of people who lived in "the west", but when laid out like this I hope its problems become apparent. All three of these people, despite being sincere Christians, had very different worldviews and understandings of what made up the "moral life". Benjamin Lay was a colorful eighteenth century Quaker who dedicated his life to the opposition to slavery (as well as other causes, like vegetarianism). All of his writings were absolutely shot through with Christian language and concepts, one tract was memorably titled "All Slave-Keepers That Keep the Innocent in Bondage, Apostates!" This would be an obvious example for Tom Holland I am sure, but the complicating factor is that the reason Lay called slave traders "apostates" is that they, too, were Christians. Even his sect, the Quakers, was by no means united in opposition to slavery--perhaps the most famous and influential of them, William Penn, himself owned and traded in slaves.

Or to give perhaps a more broad example, I have personally found the English Civil War fascinating in part because it was a conflict that was on the one hand about fundamental questions of social organization and the structure of politics, and at the same time it was about worship and the structure of the Church (one might say it is both fully political and fully religious). At times there is a stereotype that it was between the dour, religiously fanatical Puritans and the more freewheeling, decadent royalists, but this of course misses the entirety of it. Charles I was devoutly Christian, everything he believed about the monarchy tied back to his fundamental beliefs in God's will. But, of course, John Pym was also devoutly Christian, and believed in a very profound way that the path he took was the one marked by God. Every single person who killed and died at Nasby did so under the banner of God's will.

To say the English Civil War was influenced by Christianity is a gross understatement, but "Christianity" as a concept also does not have much in the way of explanatory power for the conflict simply because it does give you much explanation as to why any one person did any one thing. Now take the difficulty of pinning down "Christianity" as influencing both Lay and the slave traders, or both roundheads and cavaliers, and blow it up to the entirety of "Western Civilization".

This is where I think social theorists can be particularly helpful. A very sophisticated version of (what I assume to be) Holland's argument is Weber's idea that Protestantism provided the "spirit of capitalism" but of course this is a much more narrow argument than "Christianity shaped modern morality". But against that are materialists, perhaps most famously Marx, who argued that ideologies can best be understood as shared explanations that justify particular social configurations rather than something that actually shapes them. I do not mean to support the vulgar version of this in which ideology (in this case Christianity) is merely a set of words and phrases that can be used to support anything, but more that trying to treat the English Civil War as a sort of theology debate with swords will not actually get you very far.

Or to give a short summary, obviously Christianity was important, but the statement "Christianity was important" is not actually very helpful in understanding the history of "the west", and academics disagree quite a bit about how to define its role.

(I should also note that the straightforward equation of "Christianity" to "the West" is quite problematic, particularly when one considers eg Ethiopia)