Per http://www.spiritualteachers.org website, the origins of Neo- Advaita may traced to to certain misinterpretations of Shankara; with some allegiance to the more nihilistic-oriented teachings and/or comments of Ramana Maharshi and Nisargadatta Maharaj.
A key point of most Neo-Advaitins (Ramesh Balsekar, Eckart Tolle, Byron Katie, Gangaji, Andrew Cohen**...etc) is that one should constantly question one's beliefs: an assertion obviously contrary to MMY's approach. A quote from Nisargadatta Maharaj: " I offer to you the following dialog from Nisargadatta Maharaj... Nisargadatta: "To go beyond the mind, you must have your mind in perfect order. You cannot leave a mess behind and go beyond. He who seeks Liberation must examine his mind by his own efforts, and once the mind is purified by such introspection Liberation is obtained and appears obvious and natural." Q: "Then why are sadhanas prescribed?" Nisargadatta: "Freedom to do what one likes is really bondage, while being free to do what one must, what is right, is real freedom." Q: "How can the absolute be the result of a process?" Nisargadatta: "You are right, the relative cannot result in the absolute. But the relative can block the absolute, just as the non- churning of the cream may prevent butter from separating. It is the real that creates the urge; the inner prompts the outer and the outer responds in interest and effort." "You seem to want instant insight, forgetting that the instant is always preceded by a long preparation. The fruit falls suddenly, but the ripening takes time." "The way to truth lies through the destruction of the false. To destroy the false, you must question your most inveterate beliefs." ** on Cohen, though he's in the Neo-Advaitin category (being a former disciple of HWL Poonja - the most notorious Father of Neo-Advaitins), Cohen has (along with Wilber) subscripted to a more progressive orientation called "Evolutionary Consciousness". The problem is that he hasn't come up with anything really new! My POV: as hinted at in the website, Neo-Advaitin-ism is a type of shell-game...for losers and easy marks. Learn about it but don't get sucked into it. t get.