There is no doubt a retreat, or migration as it were, of evangelicals has taken place from engaging with doctrine, but insofar as doctrine is still present for many evangelicals of a certain era anyway, what informs them most, at least hermeneutically is the hermeneutic known as Dispensationalism. It was this hermeneutic that I was groomed in myself, not only as a kid, but in and through Bible College and Seminary (of the Progressive sort).
Dispensationalism, without getting into all of the nitty gritty, is a hermeneutic that prides itself on using the ‘literal’ way of reading Scripture in a ‘consistent’ form as they claim; it is a hermeneutic that maintains a distinction between Israel and the Church (in its classic and revised forms); and it is a hermeneutic that simply seeks to read its understanding straight off the pages of Scripture in the most straightforward ways possible (again ‘literally’ with appeal to Scottish Common Sense Realism). One of its most ardent proponents says it like this:
Literal hermeneutics. Dispensationalists claim that their principle of hermeneutics is that of literal interpretation. This means interpretation that gives to every word the same meaning it would have in normal usage, whether employed in writing, speaking, or thinking. It is sometimes called the principle of grammatical-historical interpretation since the meaning of each word is determined by grammatical and historical considerations. The principle might also be called normal interpretation since the literal meaning of words is the normal approach to their understanding in all languages. It might also be designated plain interpretation so that no one receives the mistaken notion that the literal principle rules out figures of speech….
The Dispensationalist’s hermeneutic springs then from a philosophy of language that holds to the idea that language corresponds to real and perceptible things in reality, and as such, based upon this assumption attempts to, in a slavish way (to this principled understanding of language and reality) reads Holy Scripture in such a way that comports with language’s and history’s most basic and simple and normal component parts (i.e. as it can be reconstructed through critical and rationalist means).
It is no surprise that Dispensationalism developed when it did, in the late 19th and early 20th centuries, when what it meant to do Biblical Studies and exegesis of Scripture was to engage Scripture through developmental/evolutionary criterion for reconstructing Ancient Near Eastern (ANE) history (the periods that Biblical Scripture developed within), and using various other literary criteria for determining Scripture’s origination and the cultural-societal-rhetorical contexts that gave it rise. In other words Dispensationalism developed in a context wherein things are only true insofar as they comport with the canons of observable and empirical protocol. G.C. Berkouwer describes this development this way:
We now confront the noteworthy fact that, during the rise of historical criticism, concentrated attention to the text of Scripture was considered vital and necessary. Criticism protested against every form of Scripture exposition which went to work with a priori and external standards. It wanted to proceed from Scripture as it actually existed; it sought to understand Scripture in the way in which it came to us in order thus to honor the “interprets itself.” This is what it claimed in its historical exposition of Scripture: something supposedly free of all the a prioris of dogmatic systems or ecclesiastical symbolic. In that way justice could be done to Scripture itself.
Maybe you noticed something in the Berkouwer quote, he is implicitly noting something that happened in the 18th century—again remembering that this is the context which the Dispensationalist hermeneutic developed within and from—there was a split (as a result of Enlightenment rationalism among other forces) between doing confessional/churchy biblical interpretation/study from the kind of biblical interpretation/study that came to dominate what it meant to do ‘critical’ biblical study. This split was given formalization in the mid-1700s first by publications from Anton Friedrich Büsching and then most notably by G. Ebling; Gerhard Hasel summarizes it this way:
Under the partial impetus of Pietism and with a strong dose of rationalism Anton Friedrich Büsching’s publications (1756-58) reveal for the first time that “Biblical theology” becomes the rival of dogmatics. Protestant dogmatics, also called “scholastic theology,” is criticized for its empty speculations and lifeless theories. G. Ebeling has aptly summarized that “from being merely a subsidiary discipline of dogmatics ‘biblical theology’ now became a rival of the prevailing dogmatics.”
Dispensationalism developed within the new ‘critical’ approach to doing biblical studies, although it was attempting to still honor its pious commitment to Scripture as Holy and God’s. But it did so under the ‘Modern’ constraints provided for by Enlightenment rationalism; its philosophy of language (i.e. the literalism we have already broached), grounded in Scottish Common Sense Realism, was very so much so moving and breathing in and from a non-confessional, non-dogmatic mode of doing biblical study. Hasel once again describes the ethos which the Dispensational hermeneutic developed within:
In the age of Enlightenment (Aufklärung) a totally new approach for the study of the Bible was developed under several influences. First and foremost was rationalism’s reaction against any form of supernaturalism. Human reason was set up as the final criterion and chief source of knowledge, which meant that the authority of the Bible as the infallible record of divine revelation was rejected. The second major contribution of the period of the Enlightenment was the development of a new hermeneutic, the historical-critical method which holds sway to the present day in liberalism [dispensationalism] and beyond. Third, there is the application of radical literary criticism to the Bible …. Finally, rationalism by its very nature was led to abandon the orthodox view of the inspiration of the Bible so that ultimately the Bible became simply one of the ancient documents, to be studied as any other ancient document.
It might appear that what was just described sounds nothing like who the practitioners of the dispensational hermeneutic are (i.e. evangelical Bible loving Christians). That would be correct, but the point is to note that dispensational hermeneutes don’t ever really abandon the Enlightenment principles nor the split from confessional hermeneutics that the Enlightenment produced between the disciplines. Instead dispensationalism attempts to work with and from the material and rationalist principles provided by the Enlightenment; primarily meaning that the Dispensational hermeneutic hopes to be able to go immediately to the text of Scripture, through its grammatical and historical analysis under the supposition that biblical language simply functions like any other literary language does under its plain and normal meanings without any pretext or reliance upon its (potential) theological significance. Instead its theological significance can only be arrived at after abstracting that out from the plain meaning of the words of Scripture.
John Webster summarizes what happened during this period of development this way (and what he describes applies to the development of the Dispensational hermeneutic as well):
To simplify matters rather drastically: a dominant trajectory in the modern development of study of the Bible has been a progressive concentration on what Spinoza called interpretation of Scripture ex ipsius historia, out of its own history. Precisely when this progression begins to gather pace, and what its antecedents may be, are matters of rather wide dispute. What is clear, at least in outline, is that commanding authority gradually came to be accorded to the view that the natural properties of the biblical text and of the skills of interpreters are elements in an immanent economy of communication. The biblical text is a set of human signs borne along on, and in turn shaping, social religious and literary processes; the enumeration of its natural properties comes increasingly to be not only a necessary but a sufficient description of the Bible and its reception. This definition of the text in terms of its (natural) history goes along with suspension of or disavowal of the finality both of the Bible and of the reader in loving apprehension of God, and of the Bible’s ministerial function as divine envoy to creatures in need of saving instruction.
Whenever you hear someone say they just interpret Scripture ‘literally’ dig deeper to see if what they mean is ‘literalistically’ under the constraints of what we described provided for by the Enlightenment.
To be clear, following the Enlightenment does not, of course, nor necessarily terminate in the Dispensational hermeneutic, in fact a case can be made that what the Enlightenment did to biblical studies, in some ways provided for some fruitful trajectory as well (insofar as it highlights the fact that the Bible and its phenomenon cannot be reduced to historist or naturalist premises themselves); but we will have to pursue that line later. Suffice it to say, Dispensationalism is not the pure way to Scripture that its adherents want us to think that it is. It does not spring from Christian confessional premises, and in fact ignores the fact that indeed Scripture study and exegesis is actually a theological endeavor at its heart. The only way to get a plain meaning of Scripture is to read it through the lens of God’s life revealed and exegeted in Jesus Christ.
 See Thomas Reid, “If there are certain principles, as I think there are, which the constitution of our nature leads us to believe, and which we are under a necessity to take for granted in the common concerns of life, without being able to give a reason for them — these are what we call the principles of common sense; and what is manifestly contrary to them, is what we call absurd.” The Cambridge Companion to Thomas Reid (2004), 85.
 Charles C. Ryrie, Dispensationalism. Revised and Expanded (Chicago: Moody Press, 1995), 80.
 G.C. Berkouwer, Studies In Dogmatics: Holy Scripture (Grand Rapids, Michigan: William B. Eerdmans Publishing Company, 1975), 130.
 Gerhard Hasel, Old Testament Theology: Basic Issues In The Current Debate. Revised and Expanded Third Edition (Grand Rapids, Michigan: William B. Eerdman’s Publishing Company, 1989), 19.
 Ibid., 18-19 [Brackets mine].
 John Webster, The Domain of the Word: Scripture and Theological Reason(London/New York: T&T Clark, A Continuum Imprint, 2012), 6.