Isn't this precisely what they should be doing? It's called critical thinking. The Bible, unlike a Shakespearean play, Plato's Republic or the Harry Potter series, is an anthology. It was written by a diverse group of individuals from a variety of backgrounds with a host of competing - and sometimes conflicting - agendas over the course of several centuries. Its source material spans millennia.
So when Christians ignore an injunction in Leviticus and demand obedience to a command of Jesus (or vice versa), they're doing exactly what they're supposed to be doing. They're making value judgments as to which portions of this anthology apply to them and which don't; about which texts make sense and which defy logic. Sometimes, those judgments bolster their own prejudices, such as condemnations of same-sex relationships and beliefs in eternal torment. But the core problem isn't that they're making value judgments; the problem is that many of them won't admit it.
Christians who view the Bible as, literally, the word of their god, can't acknowledge this is what they're doing because it would upset their apple cart of supposed scriptural infallibility. The fact that they do so anyway isn't the problem. It means they're human. The problem isn't the critical smorgasbord approach to the scripture, it's the claim that it's somehow infallible.
Non-Christians and Christians who look at the Bible as a product of human history have no problem praising some portions of it and condemning others. The writers of Jeremiah and John wrote under completely different circumstances with entirely different aims. Or check out the writings of Paul and the Epistle of James. The two philosophies aren't just incompatible, they're diametrically opposed.
The critical mind recognizes this, and the honest mind doesn't try to reconcile it. The problem lies with the believer who tries to have it both ways. On the one hand, he admits that divine commands for wholesale genocide in the Old Testament aren't particularly moral and, but on the other, he insists that the biblical anthology is infallible.
Cognitive dissonance? You betcha. George Orwell called it doublethink: "the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them."
The way to resolve this, however, isn't to stop viewing the Bible (or any other document) critically. It's to stop insisting on applying impossibly high standards such as infallibility to it. Such standards do provide a sense of false security, which is doubtless why they're imposed, but the resulting exercise in doublethink more than offsets it with a very real sense of insecurity that leads people to rationalize inherent contradictions - and lash out at those who expose the absurdity of those rationalizations.
Read more about these problems and others in my book Requiem for a Phantom God, available in paperback, as well as on Kindle (http://amzn.to/10nx028) and Nook (http://bit.ly/XjoCWd).