You are begging the question here assuming that morals simply 'evolve' naturally.
Historical evidence also shows very clearly that you cannot isolate 'culture' from religion, and simply say that 'Christianity followed'.
Wrong area of focus.
Looking at what happened to 'most Christians' is far less meaningful than looking at what actually drove the successful abolitionist movements.
Anthony Benezet’s propaganda campaign had its most pronounced impact in Great Britain. Nowhere else among the major slave-trading powers did a popular, public campaign against the traders emerge. That this campaign crystallized in Britain at the close of the eighteenth century might seem odd at first glance. In the second half of the eighteenth century, British merchants were the leading slave traders in the Atlantic world. There were good commercial and political reasons to favour a continuation of the trade.
Antislavery sentiments, moreover, did not always lead to antislavery commitments. That seems to be one lesson that arises from the history of antislavery thought in France, where there was a critique of the trade’s inhumanity but only the most minimal attempt to address it (Seeber, 1937; Miller, 2008).
It would be a mistake also to attribute the new antislavery campaigns to the cultural consequences of merchant capitalism, as the historian Thomas Haskell once proposed, given the complete absence of abolitionist organizing in the Netherlands, where merchant capitalism was strong (Bender, 1992).
A number of historians have detailed how the first British abolition campaign came to fruition in the 1780s – the Quaker petition to the House of Commons calling for abolition, the alliance between Quakers and Evangelicals that culminated in the formation of the London Committee for Effecting the Abolition of the Slave Trade in 1787, and the series of investigations and debates in parliament that raised and then thwarted hopes before the somewhat sudden achievement of abolition in 1807 (Anstey, 1975; Oldfield, 1995; Jennings, 1997).
Only recently, however, has the prior transition from antislavery thought to antislavery action received close scrutiny. The formation of antislavery commitments in the British Isles during the 1780s depended in part upon the changing politics of empire that attended the expansion of British dominions after the Seven Years’ War and the loss of 13 North American colonies in the American Revolution.
A new concern developed in this period that imperial practices needed to be assessed against the standards of virtue and liberty. Among Quakers in England, and among aspiring young reformers within the Church of England, Thomas Clarkson and William Wilberforce most notably, turning the nation against the Atlantic slave trade looked to be one way to improve the moral character of overseas enterprise and to foster a greater commitment to religion at home (Brown, 2006: pt III, IV).”
Heuman, G, Burnard, T. - The Routledge History of Slavery
