Sometimes we act like the scientific method was only invented a few hundred years ago. Don't you know that even an absolute savage seeing a thin tree spanning a narrow river would use something like the scientific method in deciding whether to cross at that point? He'd probably figure in his mind whether the the tree would bear his weight. He'd test it near the bank. He might get as far out as he could without totally committing and then come back. If he were really ambitious he might even roll a heavy log out onto the tree to see if it would hold. Then, he would take his data and decide whether he should cross. That's scientific thinking and it's been going on probably for as long as there have been human beings.
We like the scientific method. I'm a devout person, but I prefer knowledge vetted via the scientific method to any other kind. I think everyone does. If I hear about someone claiming to have been healed of cancer, I ask whether they've had it confirmed by a doctor and some tests. Anybody who tells you they don't like knowing things scientifically is probably lying. The scientific process is a good thing.
However, the scientific method is really limited in terms of what it can tell us about life and how to live it. No matter how much we learn about the natural world and how it works, the simple fact is that science has zilch to say about most of what we talk about in politics. For example, there is a lot of passion on this website about the policy the United States takes toward dealing with poor people. What does science have to say about that? Is mercy a scientific matter? Is compassion? The truth is that virtually all of us want to see the poor better off, but if we try to discuss why that should be, science just won't much enter the picture.
Science helps us figure out how to do things we want to do, but it is very little aid in figuring out what the wants are. Does science say whether we should have an anti-poverty policy? No. Does science say whether we should be aggressive or pacifist in our foreign policy? No. Does science say whether we should rebuild Iraq? No. Does science say whether we should have an affirmative action policy or that we should have ended slavery? No. Science is blind to most of politics and not surprisingly, to much of life.
Values help us figure out what our wants are. Things like freedom, loyalty, brotherhood, mercy, love, bravery, honesty, commitment, etc. Now, there are different ways to decide what your values are, but none of them are dead-on scientifically rational. I'm sorry, but it's true. This is why we get jarring statements like the one from Richard Dawkins the atheist who tells us he is a passionate Darwinist (and atheist) who is just as passionately anti-Darwinist in his politics. He is telling you that scientific knowledge about the world won't resolve the issue of your politics and for once, he is right.
What will resolve the issue of your politics? The answer is that you have to think about things like what is the nature of human beings, what is good for human beings, what does good even look like, whether something like evil exists and if so what qualifies as evil, what should you care about, what should government care about, etc. In figuring out your politics you figure out yourself. For most people, that process includes thinking about what God thinks and looking for clues to answer that question in religion. It should be clear, however, that those who do not look to religion to help answer these questions are no more rational or scientific than their religious co-seekers. Both persons or groups of persons, religious and irreligious, are filling their cups of value with something and they are not doing so on the basis of scientific analysis.
I think that is the substance behind Ann Coulters's claim that left-liberals are religious. They are engaged in the experience of determining their values and they do so in a way that is no more logical or reasonable than those who are religious. This is the ineffable territory of the soul -- defined as who you are.
This inability of science to provide any warrant for our longing for things like justice, good order, compassion, fairness, truth, etc. leads us to where we are and have been for some time. Despite the moniker "political science" we have no science of determining political (or personal, for that matter) ends. Thus, we accept the non-mathematical precision presented us by politics (as did Aristotle) and try to reason from experience and observation about ourselves and society. Natural law tries to deduce our morality in this way.
Religion enters the picture either as a mystical dropping out, a dismissal of the earthly world as an illusion, or (more relevantly) as a massive claim upon history. This last is what we encounter with the Jewish and Christian faiths in particular. Both say "This really happened (the giving of the law or the resurrection of Jesus)" and "Because this thing happened we can draw the following conclusions from it." The Christian faith in particular offers us this way out of the conundrum of little-explained or mysterious values.
The first kind of religion, that which drops out, is in fact irrational and proudly so. The latter kind, that based on a witness of real history, can only be seen as an attempt at rigorous rationality, perhaps even of the scientific kind. Thus, the Christian claims to have a better idea of what values one should advocate than others who grasp at the issue with no better guide than practical reason well beyond the parameters of the scientific method.