Rationality is the recognition that existence exists, that nothing can alter the truth, and nothing can take precedence over the perceiving of it, which is thinking—that the mind is one's only judge of values and one's only guide to action—that reason is an absolute that permits no compromise—that a concession to the irrational invalidates one's consciousness and turns it from the task of perceiving to the task of faking reality—that the alleged shortcut to reality, which is faith, is only a short circuit destroying the mind—that the acceptance of a mystical invention is an wish for the annihilation of existence and, properly, annihilates one's consciousness.—from John Galt's speech, Atlas Shrugged, by Ayn Rand.
Ayn Rand did not, to the best of my recollection, lean heavily on organized religion in her fiction, at least not to the extent that there are many Randian villains who are priests and preachers. But she wasn't unclear on her opinion of religion, as the above quote indicates. She held her fiction to be "romantic realism," or "life, as it might and ought to be." She believed that we "ought" to ignore religion and did her best to do so in her fiction.
It would be churlish to observe that, had she written books with a more overtly anti-religious message, they would have probably sold more poorly. It's equally accurate to observe that had her atheism been the primary focus of her work or the world's perception of it, then she's have been fighting a different fight from the one she wanted to pick.
Nevertheless, there it is. Rand was a virulently, essentially anti-faith as anyone who ever lived on this planet. When Leonard Peikoff rejects the Republican Party as one that has embraced theocratic principles, he is not only being true to the spirit of Ayn Rand; he is being very, very, accurate.
Nevertheless, Rand would have found plenty to dislike about George W. Bush besides his overt (and cloying) religiosity. The anti-abortion politics of the Republican Party would clearly have horrified Rand no matter how they were derived. In so many words, Rand concluded that anti-abortion laws amounted to forced pregnancy, making a woman a slave to an unborn child, i.e., putting the interests of the fetus, and the state supposedly "protecting" the fetus, above those of the woman herself. Similarly, blocking stem cell research would have been seen by Rand as deeply irrational, "faith-based," and "anti-life," not "pro-life."
Rand tended to be anti-environmentalist, partly because of the mystical stance taken by so many in that camp (and also because of her romantic attachment to the symbol of the industrial smokestack—Rand did not always "check her own premises"), but when scientists are routinely overruled and muzzled by political appointees, she would have recognized the anti-intellectualism in the matter, and would have then taken it as an opportunity to point to it as an example of why science should not depend on government support. But the general anti-science bent of Bush, the Republican Party, and the Conservative Movement generally is not a secret, and Rand would recognize the suppression of scientific reports and attempts to force the teaching of Creationism and Intelligent Design as all part of the same theocratic bias.
As for Bush's doctrines concerning business, well, there's a cute subject.
Rand's "Heroes of Capitalism" as my commenter Black Dog Barking names them, were not the recipients of special favors and crony capitalism. Rand disdained those who made money via political connections, no-bid contracts, fraudulent behavior, and other tricks that violated her notions of what constituted laissez-faire. For Rand, laissez-faire did not consist of "giving businesses whatever they wanted." She argued, for example, against "right to work laws," which banned the so-called "union shops" as a breach of the right to contract. Rand frequently claimed that all corporate monopolies were the result of government intervention in the market (which is technically true, given that private property itself is the result of government intervention, to say nothing of the existence of the corporation, but I digress).
Rand condemned such business luminaries as Jay Gould, Thomas Durant, Harry Sinclair, Joe Kennedy, and all others who made their money through manipulation of legislatures or fraudulent tactics rather than, well, whatever else it was that Rand had in mind as heroic. She was ambivalent about Cornelius Vanderbilt; sure, he bribed legislatures, but he also said, "The public be damned" (well, sorta), and Rand liked her businessmen unrepentant. Her real railroad hero was J. J. Hill.
The business career of George W. Bush is nothing but crony capitalism, a series of essentially failed business ventures set up through his family contacts (many of them when his father was President of the United States; consider also the business history of brother Neil), all but one one leaving GW richer, and some investors poorer. His one singular success, the Texas Rangers baseball franchise, gained most of its value when the city of Arlington, Texas used its power of "eminent domain" to seize land for a new baseball stadium, paying the original owners what was later judged to be less than 20% of the actual value of the land.
Yeah, there's a real "Hero of Capitalism."
So, G. W. Bush, crony capitalist, faithful believer, and a man who brags about making decisions based on his "instincts," which Rand would have branded "whim worshiping."
As for the war in Iraq, Rand was militantly against the Vietnam War, condemning it as an ideological affair that did not involve the proper interests of the United States. Would she have fallen for the "9/11 changed everything" argument, and said that it was fine to use an atrocity committed by persons from Saudi Arabia, Egypt, Lebanon, and the UAE as an excuse to invade Iraq, the one secular holdout in a theocratic region? Would Rand have supported Bush's "Crusade?" Would she have decided that "the end justifies the means," and supported warrantless wiretaps, extraordinary renditions, torture, denial of habeas corpus, "stop loss" orders, and the entire litany of totalitarian methods now used by the U.S. Government in the name of "security?"
She would have said, "Whatever you think that 9/11 changed, it did not change lies into truth, or irrationality into reason."
The real question is why so many people, including avowed Objectivists, think that it did.