On some occasions I have thought of writing on this subject, e.g., when I read a brief passage in David Parker's An Introduction to the New Testament Manuscripts and Their Texts (CUP, 2008), especially since I haven't said much on the topic myself (in contrast to other ETC bloggers).
So I guess I will start with David Parker's brief note (p. 187):
The obvious significance of the connection between one’s wider understanding of history and human society and one’s attitude to textual criticism will be more clearly illustrated to someone working in the theological milieu by examples of a quite different point of view.
For an example of an approach to New Testament textual criticism with an equally explicit ideology, see the website ‘Evangelical Textual Criticism, a Webpage Promoting Textual Criticism of the Bible from the Perspective of Historic Evangelical Theology’ (www.evangelicaltextualcriticism.com/), claiming among others for evangelical textual criticism the characteristics that
It approaches the task of identifying the words given by God with reverence and therefore caution.
It approaches the task of identifying the words given by God with a confidence in God’s provision.
It is not clear whether this providence is seen in the way in which the text has been preserved or in the work of the textual critic (or both),...
For the specific question how providence is seen, I personally would refer primarily to the way in which the text has been (sufficiently) preserved. On the other hand, I agree with David in general that it is not clear what this approach actually means,and I actually think I like it to stay that way. Perhaps it is easier to say what evangelical textual criticism is not. For example, in a comment to a guest post by James Snapp, Peter Williams (blogfounder) says:
Members of this blog represent a variety of approaches by evangelicals, and that's how it should be. There are various possible interpretations of the evidence that are compatible with historic evangelical theology. However, there are also some approaches that do not sit well with such theology (and scholars will therefore either challenge the approaches or the theology, or both). Thus we may at least define our approaches negatively: they are not X, Y, or Z. For instance, Von Soden's preference for 'Joseph begot Jesus' in Matthew 1:16 on the basis of the Sinaitic Syriac was wrong philologically, but even before a demonstration of its philological error was available, it looked wrong-headed to evangelical (and other) theology.
Peter Head, on the other hand, once suggested in a blogpost that one "cannot have an 'evangelical' textual criticism, when there is no consensus of what an evangelical position is on this topic." He further stated that
If a site like ETC is to have a goal it should work toward a consensus among evangelicals which should rule out some DIY approaches and agree on some parameters arising from an evangelical concensus on the inspiration and inerrancy of Scripture, or is there no consensus on that doctrine among evangelicals?
I doubt that there is a consensus doctrine and I would not want to work out one. For me Dirk Jongkind's ""basic tenets of evangelical textual criticism" are more than enough:
I think there are three basic assumptions that characterise evangelical textual criticism (each with their own modifications and refinements, but we are not going to bother with these).
1) There is an 'original text' to aim for in New Testament textual criticism.
2) There is the theological conviction that the preservation of the New Testament is sufficiently reliable.
3) The canon of the New Testament is (in one way or the other) a real and given entity.
These basic tenets give room for "a variety of approaches" (PJW), interpretations and problematization (cf. the various comments to Dirk's post).
To add my personal thought on 1), I prefer to use the term "initial text." I regard the reconstruction of the initial text as an on-going scientific enterprise (which is on-going), whereas the acceptance of the simplest working hypothesis, that the initial text essentially represents the autographs is a matter of faith. There are many other related and complex matters; for example, I agree with Ulrich Schmid who has pointed out that we cannot deal with individual writings and neglect that they have been transmitted in collections. At least one person (the collector) has affected the book in terms of editorial activity.
In November 2008 I was involved in some related discussions with Bart Ehrman and others on Wieland's textual criticism discussion list if anyone would want to read. There are two or three relevant threads ("Initial text and exegesis" and "Analogy and internal evidence" and perhaps "99.5% Reliability and the 'Dark Age' of the Text"). I suppose you can find them at the bottom of this page.