I've never heard of the book myself, unfortunately. But just because a historian wrote about this premise (which was unfortunately not cited in the Science paper anyway), does not mean it's accurate. The problem is that it flattens all of medieval Europe https://twitter.com/pseudoerasmus/status/1192860240330592257 …
Also, they seem to have not acknowledged the presence of the Church in N Africa and the ME, but they mention the early period of Christianity where it was in fact very widespread in those places.