My knowledge is limited Briggs, but it's as far as i know one of the very reputable major schools of Hindu Vedantic teaching that emphasises non-duality.
http://en.wikipedia.org/wiki/Nonduality They teach that only God or Brahmin is real, that all of the relative or dualistic time/space stuff that we perceive as reality is ultimately unreal.
That's the topic that has been the subject of much discussion here. My understanding is that in many ways like Buddhism it teaches that even though the relative reality is 'unreal', and a creation of the ego (individual and collective) that ultimately we have to guided by teaching to engage correctly with it in ordinary life in order to eventually transcend it. That it's (ordinary life) important and can't be ignored.
This article outlines a problem that has developed around the popularised ersatz versions sometimes seen in the West which with comments like 'we're all enlightened' ignores the view of most that there seems usually to be a long road involved in reaching the state where duality and individuality may be transcended:
http://www.angelfire.com/realm/bodhisattva/aziz2.html There's teachers around who essentially teach from an Advaita-like nondual perspective all the time - like Tony Parsons
http://www.theopensecret.com/index.shtml He draws in a very specific way on this perspective in his teaching:
http://www.youtube.com/watch?v=T5-zMV1x6q0It produces a style of teaching which as a result of his always pointing out that the questions are coming from a personal viewpoint sounds like continuous put downs of his questioners. He may well be a realised teacher, or may not. I'm unsure.
If misused non dual teaching can be misunderstood. For example - yes, from a non-dual/timeless/eternal now/absolute reality perspective we all are already realised. But from a dualistic/time based or conventional view we are not - we all will eventually become enlightened, but this will take time.
The underlying logic of his approach (which is possibly representative of a certain more purist interpretation of Advaita teaching that seems to be around) is I think that it's regarded as a mistake to get involved in discussing or working with stuff from a relative personal path perspective, as this just reinforces and augments ego. (the package of beliefs that create the illusion of selfhood and the reality we inhabit, and the idea that there is a path to becoming enlightened)
The teaching is that we're as a result of our mistaken view naturally inclined to think in terms of striving and path. But that this striving is itself just another form of the grasping after or attachment to mind made conceptual realities that keeps us locked in this reality. A failure to remain 'in the now' as Eckhardt Tolle might put it - we get identified with chasing after an imaginary future state that can never come into being as a result of our identification with it. (a sort of existential catch 22)
There's also a view that religious institutions tend to emphasise path because as purveyors of the tools that allow us to 'progress' along the path it gives them power.
The flipside is that it's tempting to conclude 'well then there's nothing I can do to progress spiritually'. My personal sense is that this isn't true. (see below on fear and stress)
Completely avoiding engagement with ego stuff is possibly a bit of a tall order, in that even language is structured in a way that that presumes this personal/relative view. The idea I think is that if we stop reinforcing ego it increases the possibility that we may awaken. i.e. drop these delusions, revert to a non dual consciousness.
The likes of Buddhism and I think Advaita in its original form (correct me if I'm wrong) would agree that striving or grasping after spiritual objectives is counter productive, but that on the other hand correct use of practices like meditation, teaching, reflection and so on (i.e. without striving - possibly a tall order too?) help to speed progress.
The logic being basically that unless we get our lives reasonably under control so that we are not overstressed and riven by raw fear into creating a crazy, selfish dog eat dog environment that forces us in order to survive to act in a way that will provoke fear in others, the chances of our creating enough space/calmness in our minds to enable the sort of intuitive leap realisation requires is minimal.
It's a very tough issue to bottom, and one that I personally struggle with.
Most that achieve something regarded as enlightenment seem to get there via some sort of spiritual path. Experience suggests that spiritual practices like meditation do deliver changed consciousness, marked by breakthroughs of one sort or another like e.g. calmness, insight, the release of emotional blockages.
Yet many report that the real breakthrough only occurred when they finally despaired and gave up the path, gave up striving.
Buddhism teaches of path as being like a raft you use to cross a river on your way to a city. Having reached the far shore one has to leave the raft (teaching) behind to get to the destination.
That spiritual practice somehow can get you into a zone where the likelihood of the great 'ah-ha' moment or leap of insight occurring is more likely, but that ultimately we have to release this too as you can't fight fire with fire, or transition to a new reality by means of the logic of the old .....