To give a really really simplified version on those three, here goes.
All three, in one way or the other come to grips with the modernist turn in philosophy, the critical turn, initiated by Immanuel Kant.
For Kant, the categories of the mind co-construct the perceived world, so the world we experience is in part a construct of our own mind in-forming its own stability and coherence onto an otherwise chaotic plenum.
This philosophical move had massive implications for Christian theology, which in its Scholastic phase was predicated on a naive realistic view of the world–our minds are like mirrors, passive recepients of the “real” world out there. [The same holds true for the mystical sects who interpreted their otherwise trans-rational experiences as giving a glimpse of the "real" transcendent realm of heaven or whatever. More on that in another post].
For Kant then the human mind could not naively describe the trans-rational realm (transcendelia). Thus metaphysics (from Aristotle-Scholastics) was killed. If the human mind therefore could not point up to the transcendent, there was only two choices for the transcendent to interact with the human rational.
1. If transcedence could not be experienced by the conscious mind, then Spirit was to be located in the unconscious (subconscious) mind.
2. The rational mind could not point to Spirit (from Kant). The unconscious mind was full of sin and separation. There was no way that we come up to God–rather God must come to us from without/above. God must break through our rational frames in an non-rational (ir-rational) frame that must respond with its own “ir-rationality”, namely faith.
3. The rational mind could not get to Spirit, neither the unconscious. But the existential outlook of #2 is a subtle, revived humanism. Only a return to the fundamental doctrines of faith will guide us. And/or a personal conversion of the will in accepting Jesus Christ as Savior.
Position 1=Modern Liberal Protestantism (from Schielermacher). Also the Romantics and Jung fit into this category. The most obvious weakness of this position is that the unconscious is not necessarily trans-conscious but in many cases is unconscious, sub-conscious, egocentric narcissism. Not transcendental bliss.
Position 2=Neo-Orthodoxy. Barth and the Fideism of Kierkegaard. Very existential, good sense of the need for choice of faith in this world. Downsides: no proof, overly cerberal (to the detriment of ritual, sacraments, mysticism).
Position 3=Fundamentalism and Evangelical/Born Again. A modern response to the secular modern world attempting to “prove” the mythic world. Protestant fundamentalism is often (unconsciously) wedded to a purely modern notion that history/science is the truth. That something is “true” only if it “happened”, only if it can be studied with the five senses, has material causes, etc. So fundamentalism, say with its turn in creationism, attempts to prove the Bible is scientific theory. Too many downsides to name really. But obviously a retrenched premodern value/worldview using the tools/cognition of the modern (formal operational) world.
Obviously totally unopen to any criticism, questioning, or interpretation. In the modern frame, there are no “interpretations”, just the Myth of the Given parading around as the one and only “Truth.”
All three of these options are deeply flawed as it comes to the question of Christian mystical theology.
All share the classical Protestant fear of anything in Christianity being “non-biblical.” So mysticism for many a Protestant is in fact not a Christian practice at all but a Greek, pagan import into Christianity.
Modern Liberal Protestantism is open to transcendent experience, but as mentioned, committs numerous pre/trans fallacies–seeing anything non-rational as inherently trans-rational. When in fact much of what is non-rational is in fact sinful, arrogant, self-centered pride. Modern Liberal Protestantism failed in large measure because of its weak understanding of the destructive power of sin and human evil in the world–particularly in the face of the savagery of the Two World Wars. The Liberal Protestant wing in the 19th century influenced by Hegelian optismism, envisioned the 20th century as the dawning of an age of peace and prosperity. Instead the bodies keep pilling up across the planet. The death train is running full steam ahead and does not appear to be slowing down anytime soon. To this incomprehensible display of degradation, Liberal Protestantism, in some cases morphed into Political Liberation Theologies.
These postmodern theologies (Feminist, Environmentalist, 3rd World Liberationist) attacked the dark sides of the modern world. Influenced by Marx, Freud, The Frankfurt School, Buber, Heidegger, they used the rising injunctions of deconstruction, social criticism, hermeneutics/structuralism, to criticize the foundations of Christian theology and ecclessiology. They argued that a Christian theology-church structure that does not consciously stand up against the modern death train, materialism ethos, and capitalist-military-industrial complex is beholden to this system. They realized rightly that all theologies are enmeshed in social-political-class contexts, and if not properly examined and made transparent, unconsciously legitimate and support certain classs/social structures–usually unjust ones.
And this political-liberation critique (also found in Catholicism) has been very effective against the inadequacies of the traditional and modern approaches to theology, both liberal and conservative. But in terms of mysticism, this camp has (mostly) forgotten the great path of Christian purification, illumination, and union. There is often talk in these circles of deep spirituality being the antidote to materialism, apathy, and meaningless in the post/modern worlds, but the alternative is not fleshed out in any real depth.
Neo-Orthodoxy, as formulated by Barth, was inherently anti-mysticism. Neo-Orthodoxy had a much more accurate view of human sinfulness but simply believed we were so fallen that there was no way to be brought up–no deification, no sanctification, no devotion, nothing.
Fundamentalism is also anti-mystical, seeing it not as one of the “fundamentals of the faith.”
Evangelicals are also open to (temporary) mystical experiences. Whether Pentecostal Charismatics, Evangelical Tent Revivals, or gospel-music induced ecstasy in a Black Church. Also, all of those—particularly Evangelical Revivals among whites–are also prone to the pre-trans movement, when the temporary states are not higher altered states but temporary regressive states in a socially sanctioned format. For Example: Christian heavy metal concerts.
So while some of those have mystical-ish moments, there is no fertile ground for healthy, long term transformation in any of those theological schools.
If we go back to Kant, we see the reason why. Notice that all three are perpetually focused on rational and pre-rational, but have no sense of trans-rational.
Kant himself said that the human mind could only experience phenomena (the product of human mind/environment construction) and never noumena (the thing-in-itself). But this chasm was Kant’s mistake.
How could his mind know that it can’t know the thing-in-itself—presumably therefore his mind would have had a notion of what the thing-in-itself looked like. Also he postulated that he understood the categories of the mind. But how would the mind, unaided, know of the categories by which it understands?
What part of Kant’s consciousness “saw” the categories?
And so Kant was criticized (rightly) by the Idealists from Fichte on, who knew that the Pure Ego (of Fichte, i.e. the Witness) was the part of us that understood the categories of the mind. This trans-rational aspect of ourselves which can be accessed through interior practice helps co-constcut the higher levels of evolution and allows access to higher states of conscious (mystical ones even) at any level of development.
So the modern/postmodern Protestant theologies (and Catholic ones too for the most part) have not understood a post-Kantian modern mystical theology. Which is again not to say individuals do not have such states–of course they do–they simply have no frame with which to adequately interpret them and help them sustain the enduring insights gained therefrom.