My general view is that the most significant current right-wing threat to liberalism is nationalism, with religious integralism a very distant second. However, the latter is still worth considering, and it and nationalism often intersect in various ways. It is probably no accident that many authoritarian nationalists (Putin, Orban, Erdogan, etc.) also promote reIigion-inflected social conservatism.
I also tend to think integralism is intellectually weak, much like nationalism. It strikes me as easy to refute (indeed, the job was largely done by early Enlightenment liberals). In general, I have somewhat more intellectual respect for the left-wing enemies of Enlightenment liberalism than the right-wing ones (though the latter do sometimes pose a grave political threat; a movement's political success often has little connection to the quality of its ideas). But perhaps Kevin will persuade me to rethink that, or at least view integralism with less contempt than I do now.
In any event, I can't wait to read the actual book, which I have now ordered.