Without God, people in the West often become less, not more, rational. It was largely the secular, not the religious, who believed in the utterly irrational doctrine of Marxism. It was largely the secular, not the religious, who believed that men's and women's natures are basically the same, that perceived differences between the sexes are all socially induced. Religious people in Judeo-Christian countries largely confine their irrational beliefs to religious beliefs (theology), while the secular, without religion to enable the non-rational to express itself, end up applying their irrational beliefs to society, where such irrationalities do immense harm.There are several problems with Prager's above claims. The first and foremost is that it portrays a deep ignorance of the history of philosophy. All the secular irrational doctrines had their origin in religious and theistic thinkers that severely undermined the efficacy of reason. Philosophers such Rene Descartes (a Catholic) and Immanuel Kant (a Lutheran), among others, did much to undermine reason and the secular thinkers that followed them simply pushed their ideas to their logical conclusion with the ultimate result being the absurdities of 20th century philosophy. The result of the decay of philosophy was a deterioration in all the humanities and arts. As philosophers claimed to have conclusively shown that no absolutes and no standards existed, it is no surprise to see the obvious results on art and language.
But there is no reason to think that secular rational and principled people that speak politely, produce great art, and think clearly about important issues cannot exist. I dare say I know quite a few myself. The culture does not have to continue to be dominated by ugliness, coarseness and irrationality but it seems to me that substituting one kind of irrationality for another is hardly a reasonable solution.
As to the particular irrationality of regarding humans and animals of equal value, I don't think that opinion is limited to secular thinkers. Certain religions of the East also take this view. If one understands that value for human beings depends on holding man's life as the standard and man's happiness as the goal of life, then I think there's really no issue at all. Admittedly this is not self-evident but thanks to Ayn Rand, the means of establishing objective values has been achieved. Animals may have value for man, but they are not of the same value to man as man.
This series concludes with Part IV.
Update 8/24/2008: Added link to Part IV.