some of the people who do it aren't religious believers. this is a new thing, and in many ways, it's a particularly good thing. it keeps the religious believers honest when they talk about the texts. :)
on the other hand, all of them--whether believers or not--share a sort of respect for the text, an interest in entering into the world-view, even the psyche, of the writers, a desire to see the world as they do, and a general sympathy with them. and, indeed, not just a sympathy for authors, but a sympathy for communities, for religion, for the kinds of folks who write these kinds of texts.
and that, i think, turns out to be necessary. it's not religious faith that's necessary; rather, it's a kind of basic sympathy with the project. it's reasonable to have a distanced suspicion of the text, but only to a point. at some point, suspicion of the text impedes the ability to read it, and the result is bizzare and unfruitful interpretation.
this is especially so when the suspicion of the text arises from some external concern. if a suspicion of religion, or a rigid marxist analysis of class, or an ossified world-view prevents seeing things in a new way, then texts as challenging as the bible are going to be impossible to enter.
this isn't unique to the bible or other religious texts. i think it is shared by the classics of philosophy, or epic poetry, and certain sorts of novels too. it's why i can understand and resonate with theravada buddhist literature, even as i am not a believer in that context, and by contrast, why some people dominated by a master narrative understanding hostile to religion may be unable to understand any of them.