Liberalism itself divides into at least two categories. One is to be liberal about something, and one is to be liberal in a constitutional or freedom sense. For example, being liberal about Christianity means being other than, less than perhaps (in terms of beliefs), the given orthodoxy of the day or some previous period. Yet it can also mean acceptance of the right to vary belief, even if this particular individual has not varied belief from a given orthodoxy. Usually, however, they go together.
It follows that this variation of belief is either a matter of subjectivity or it is a matter of being consistent with a different objectivity than provided within the orthodoxy. So, for example, the variation of belief is a personal preference, worked out for oneself. However, it could simply be a clash of objectivity: that scientific objectivity, or social scientific objectivity, demands variation of belief from Christian orthodoxy.
Incidentally, there is no agreed basis of what is orthodoxy, which is a standard of belief. It varies between deonominations and it varies within them. One group's orthodoxy is another's heterodoxy. So here it is variation - usually doubt about - from an orthodoxy however it is defined.
All that deconstruction involves is understanding. It means reading between the lines and employing techniques of "differance" (as Derrida called it). In other words, the text becomes understood as constructed, as a free-floating narrative, that it performs but is not objectively rooted. Even if it is not so rooted (in culture, history, binary language, some foundations of God), and just performs, and is a narrative for whomever it suits, then it can still be presented as such, as it was (when it was believed to be so rooted).
This is what the postmodernist John Milbank has done. He takes the tradition lock, stock and barrel, but understood as in a postmodern space. He was taught by Rowan Williams just before Williams became Archbishop of Wales. Williams does not follow the Radical Orthodoxy of Milbank, but he and Milbank overlap in the place of narrative in their theologies, and the impact of Hans Urs von Balthazar on both. Radical Orthodoxy, like Balthazar's thought, is postsecular as well as non-objective in any worldly sense, and into that postmodern space is placed premodern Christianity - frozen according to the point the tradition is utilised. Rowan Williams uses narrative to write about the Christian story in intense detail. Both appear orthodox, and appearance matters, but there is something not quite full as in the days of Christian culture from where this orthodoxy was plucked, as it had developed to that point.
These are definitely postliberal, even though both theologians take something of the freedom or constitutional liberalism in order to have the right to promote their versions of shifted orthodoxy.
Postsecular theologians continue to use the word God, and indeed all the other Christian words. At times it is as if the God is just as the old God, and is like a light from the old window into the postmodern bubble. However, that God is just as contained within the bubble as all the other text. That God is subsumed into the liturgy. What is real, such as "real presence" isn't quite so real as real. It is like inhabiting a virtual world where everything is the same except it is in a mirror reflecting spacetime from the past that no longer exists.
However, there are deconstructionists who freeze nothing. They do not objectivise anything either. Their mirror is up to date, or indeed stretches out into a perceived future time. They'll criticise science and social science when they need deconstructing, but they will deconstruct Christianity too - and thoroughly. The tradition exists as a resource and an activity, but it is reversed in and around itself, sometimes pulled through ninety degrees, a hundred and eighty degrees and even three hundred and sixty degrees. It is a mixture of tradition used and tradition undermined (even abused). The key is advancing the inner life (though that is not an objectivity) without dualism between the Christian tradition and the rest of life (though one must allow the Christian story to be its roundabout language play - why I don't agree with Cupitt's The Old Creed and the New (SCM Press, 2007) and its dismissal of heterological language. Dismissing the narrative play and going for direct language is the mistake liberal objectivists have made.
The stream of thought for the postmodern orthodox is Karl Barth, Hans Frei and George Lindbeck. Nietzsche is important too in the background. Barth's God became so detached from culture and objectivity that Frei said the Biblical narrative is something that stands in itself and in its reading, and Lindbeck did the same for doctrine - (ecumenical) doctrine is identity through performance of what people do, that is Christians who commit to a particular role performance. Milbank intensifies this to a form of (Anglo-Catholic) Church and Christian condition. This is all frozen: the play has been written and it keeps being performed.
Above are John Milbank and Don Cupitt, deconstructionists both but very different!
The stream of thought for liberal deconstructionist is, I would say, James Martineau, who promoted subjectivity and individualism, for which the biblical narrative was just one example of faith, and where the individual conscience was greater than any book. The implications of Martineau with his subjectivity in intense plurality are postmodern. Not many know of him, but he worked out subjectivity the best. The line is surely then John Robinson and John Hick, and also Nietzsche, Altizer and Hamilton, and then into the postmodern with Don Cupitt and, from the death of God theologians only, Mark C. Taylor. When the postmodern is arrived at, the objective and subjective dissolve, and there is a new stress on language and the collective, but nevertheless individuals and groups will play with forms of religion for the purposes of pursuing the inner life. As for the inner state, this is more akin to Buddhist no-self than a subjective self. Martineau wrote about the self, but deconstruction liberals understand more about the no-self. The self too, just like the secular, is subjected to deconstruction. In the frozen form, the self also gives way to the collective narrative, that it (the narrative) provides the way of peace, whereas for the liberal deconstructionist the reduction of ego is the means of promoting the inner life towards nothing - that the purpose of all liturgical forms is simply to give oneself into the floating narrative and reduce the self. The reason why I think Martineau understood this was his emphasis on the liturgical, on the poetic, and that inevitably liturgy is more conservative in its forms of language than the belief it carries.
In both forms of deconstruction, the emphasis is on performance, on doing. It is about practice in and around the tradition, one subjected to the freezer after selection, and the other subjected to intense play. My own line is that of Martineau, Robinson, Cupitt and also Lloyd Geering (New Zealand Presbyterian version of Cupitt - more historical), Graham Shaw (Anglican, plus Quaker, user of the tradition and all its resources), Paul Lakeland (American, an overview), Jean Baudrillard (sociology, semiotics), Peter Berger (sociology - his actual religion is out of step with the implications of his sociology), Marcel Mauss (Social anthropologist), Philip Hewett (Canadian Unitarian - broad, open, humanism) and Daniel Liechty (ethics first open postliberal). There are also influences from different faiths and an increasing appreciation of John Hick and Richard Holloway.