Baber is alluding to an argument from Daniel Dennett's book Breaking the Spell -- the one about how our religious society "believes in belief." We think it's admirable to remain a believer, even if you doubt. Doubts are like the temptations that a husband or wife might resist to remain a faithful spouse. The effect--Dennett argues--is to valorize irrationality--turning away from arguments and evidence that foster doubt instead of following them where they lead. Baber is trying to pin a similar sort of irrationality on atheists--except she claims they believe in unbelief. But do they?
New Atheists believe in unbelief. For some reason they think it important to assure their followers in the village that religious belief is not merely false but uncontroversially false and that educated people who profess to be religious believers or claim that theism is compatible with science are out to dupe them.
I don't believe in belief. Beliefs about metaphysical issues, including the existence of God, are inconsequential. In the aggregate, religious believers are no better or worse than atheists and, historically, societies that have embodied strong religious commitments are no better or worse than those committed to atheism.
I would be very interested in hearing why the New Atheists and their followers believe, with such manifest conviction, in unbelief.
If atheists believe in unbelief, it's in nothing like the sense in which theists believe in belief. Atheists don't feel tempted by theism. They don't reinforce unbelief in each other by stressing the virtue of unbelief. They don't ignore arguments and evidence for theism; they pay attention and find it all lacking. Let's face it--the epistemic situation of the theist and the atheist are very different. Believing in "things unseen" is hard; disbelieving in them is easy!
So no, atheists don't believe in unbelief in the sense in which theists believe in belief. But do they believe in unbelief in some other sense? We speak of believing in X when we think X is really important, or central to our lives, or worth promoting, or worth giving additional influence. You can believe in people, or concepts, or "isms" in that way. I believe in my kids, and democracy, and moral realism (the view that there are moral truths) in that sense.
I think some atheists believe (in this sense) in atheism--particularly the crowd that's often labelled "the new atheists." They are excercised by the continued existence of religion in the world, and would like to get rid of it--even the liberal, non-literal variety. I'll leave it to those folks to answer the question Baber asks at the end, because I can't say I'm in that camp.