The very idea of “objective” knowledge (i.e., knowledge acquired through honest observation and reasoning) has values built into it, as every effort we make to discuss facts depends upon principles that we must first value (e.g., logical consistency, reliance on evidence, parsimony, etc.).While there are a number of different philosophies of science and epistemologies that can accommodate the scientific method, Harris is certainly correct that you have to accept one of them for the whole thing to work. Harris' choice appears to be scientific realism, which, in short, is the view that science describes a world that is really "out there", and that a scientific observation is true when it corresponds to this real world.
Which is funny to me, because Harris is a utilitarian. At least that's what I and Orr make of his conclusion that the good is the "well-being of conscious creatures". A quick scan of the book shows that Harris explicitly identifies identifies as a consequentialist (see page 62; sadly there's no Google Books preview I can link to). Consequentialism + a hedonic conception of the good = good old fashioned utilitarianism.
Utilitarianism, unlike some other ethical theories, has philosophical implications outside of ethics. In particular, I think it commits you to some form of pragmatism. If the answer to "what should I do?" is "whatever action maximizes the general happiness" then the answer to "what should I believe?" is "whatever belief is conducive to maximizing the general happiness". That starts to look a lot like pragmatists' argument that what is true is what is most useful to believe.
As Richard Rorty pointed out in my favorite essay of his – "Religious faith, intellectual responsibility, and romance" – this affinity between utilitarianism and pragmatism is historical as well as logical. William James was a great admirer of John Stuart Mill, and The Will to Believe can be read, in Rorty's words, as an attempt at a "utilitarian ethics of belief". And James, of course, believed strongly that religious faith could be a force for good.
This makes sense. Under pragmatism, the statement "God exists" is true if it is useful to believe that God exists. This may seem a flimsy reason to believe, and Rorty lays out a number of ways in which it limits what one can believe, but it is no flimsier a foundation than pragmatism offers for believing in science, and most would consider that foundation pretty strong. No one would mistake Quine and Sellars and Dewey for arch opponents of science, after all.
So Harris has a problem. He can be a scientific realist, which rules out both pragmatism (which rejects the idea that there needs to be a real world "out there" which true statements reflect) and utilitarianism (because it implies pragmatism). Or he can be a utilitarian, and a pragmatist, and acknowledge that religion is often a source for good in the world and a source of joy for many privately. But you can't be a utilitarian and a scientific realist, and you certainly can't try to get to utilitarianism through scientific realism, which is what he's trying to do now.