Even the stuff they say - I can at least sit down and consider it without freaking out instantly.
In some ways they resemble the very modern panpsychist school of thought (Giulio Tononi, Sam Harris). Consciousness is a basic ingredient of matter. Both matter and consciousness are real. Evolution is real. There is no biblical god. Cosmology - they defer to science when it comes to that, but having consciousness as a major ingredient does shift the perspective a bit (everything becomes "evolutionary" in a sense).
The way they think of the future reminds you of the Singularity theories. If Ray Kurzweil and Pierre Teilhard de Chardin wrote a book together, it wouldn't be far from this.
The one thing that's a bit far out is the claim that consciousness could, in theory, interact with matter directly, not just through regular mechanisms (brain, nerves, muscles, etc). They do insist it's super-hard to do in practice. They do shun the miraculous stuff, they insist that the change of consciousness is all that really matters here and now in a spiritual endeavor. In this regard they're not very far from, say, your run of the mill buddhist school of meditation.
As long as Aurobindo and Mirra were alive, they kept the place as non-cult-ish as humanly possible. I would say they even had a remarkable amount of skepticism, aside from the claims mentioned above. I'd like to visit Auroville one day, to see how things have changed in the decades since Mirra's passing.
Hard to explain. I've seen plenty of crazy places (adventurous youth + interest for spirituality, yadda-yadda), but the stuff that Aurobindo + Mirra started strikes me as remarkably... rational, I guess?
Read and draw your own conclusions.
I think that claim like this alone, is not so far stretched, when you assume consciousness comes from brain activity, ~ electricity - and with classical physics, magnetic/electric fields or even quantum physics, everything is connected and interacts - consciousness do influences matter. So when you have a different thought, a different magnetic field is the result, etc. that does influence matter directly.
The far stretch claim is, that conscious can have a directed, focused effect and not just be random.
Anyway, the idea that mind can influence matter directly(magic thinking), is a very old one and I think the majority of the world population is still holding to it. Allmost every religious person does (in a different way). And in nonreligious, educated, western people I have seen it quite a lot, too. Most are not really conscious about it, though.