Thanks, Thomas. I'm no expert but I can give it a shot.
Firstly, I'm not an advaitin, nor a person who sees Shankara as infallible. However, historically, Advaita Vedanta has been the subsect of Hinduism that has made it to the west, for several reasons. One is that many of the original swamis and thinkers who came followed the Smarta (another term for Advaita Vedanta, basically) tradition. It tends to emphasise the intellect, and debate, over bhakti. So perhaps it fits in better for the west, because of that. Less of a jump. There is still (personal belief) a subconscious aversion to 'idol worship' I think, and Advaita can be studied outside of any bhakti, yet in traditional advaita, bhakti is there, just not to the degree the bhakti schools are. There are many other schools in India, including strict Vaishnavism,. Saivism, etc. Most respect Shankara, but are not quite so enthusiastic about it as Advaitins. So, in summary, it varies. Some other schools even try to get or prove that Sankara was exclusively one of their own. In reality, the Smarta sect says that all other sects are essentially the same thing ... Siva is God, Shaktia is God, Vishnu is God, etc. So those that try that are just selective when they choose which verses of his to quote.
The other question is where neo-advaita gets it messed up. The biggest problem is the pronoun 'I'. It has two distinct meanings. The first is the ego, the personality, represented by a name usually, but also substituted by 'I' for the linguistic shortcut. Very very common.
The other 'I' is unheard of by the common man. It is the part of you that is identical to God, only to be realised. It's gotten to by persistent sadhana, meditation, and devotion, by a very rare few on the planet. Years (lifetimes) of study, culminating in a non-experience called nirvikalpa samadhi, and translated (poorly) as the Realisation of the Self. It is the culmination (what Hindus believe) of many lifetimes on this planet, when all karmas are resolved. The seers and mystics who have been there say it is not describable. Just very recently I heard it said that, 'All you can say about it is that there has been a fundamental change in perspective'. after. So mystically it's incredibly deep. Souls there would never speak about it at all, or at least very little, and would 99% of the time only talk about how to get there. So the teacher speaks in practical terms, for the benefit, of others, not in 'yapping' ways for the benefit of himself, his ego, on how much he knows.
Essentially it illustrates that at the very core of you, after the physical, emotional, intellectual, astral, and even soul bodies are all discarded, that is what remains.
Therefore, for someone who has seen both types, the neo-advaitin (who has confused these two 'I's, its actually really easy to recognise.
Hope this helps some.
