At the end of the day, the difference between something being natural or supernatural lies in its compliance with natural laws. The problem with Dune when it comes to deciding about the supernaturality of phenomena is that it gives us very little to make such a decision:
With the exception of ecology, science is hardly described in the books and in particular nobody seems to care about the meachnisms behind the effects of spice, which is the source of almost all potentially supernatural abilities in Dune.
This somewhat makes sense, as we are talking about microbiology here, which is arguably unfeasible due to the Butlerian commandmends against any kind of computer, robot or even simple automatic devices. For related reasons, the mechanisms behind potentially supernatural abilities are hardly described in the books – at best, “genetic memory” is mentioned. Furthermore, most people having potentially supernatural abilities do not perceive these as supernatural.
Hence, what seems magic to us, may have been considered a biological effect by Frank Herbert and unless he made some specific statement about this that is unbeknownst to me, we have very little on our hands to decide about this. Thus,
as I wrote before, when discussing supernaturality in Dune, a variation of Clarke’s Third Law comes to mind:
Any sufficiently advanced or weird biology is indistinguishable from magic.
Now, despite all this, the mechanisms behind some Bene Gesserit abilities were indeed described and thus they are one of the few potentially supernatural abilities for which I have little doubt that Herbert considered them to be natural:
- The Weirding Way (i.e., the ability to move very quickly) was attributed to mental and physical training. Such a training is described to some extent in Children of Dune.
- The Voice was attributed to reading the opponent’s speech and gestures and saying just the right words in the right way at the right time to crack him, i.e., what you describe as “is it rather the result of millenia of psychological science combined with training and textbook knowledge of how certain people from certain places and contexts react to certain phrases and tones”.
- Some other abilities like increased perception were attributed to mental training.
Other Bene Gesserit abilities like truthsaying, ancestral memory, transmuting poison and controlling one’s aging were not even remotely described in such a way and I thus the uncertainty described above applies to them.
Note that all of the above is based on the four Dune books only, but should also apply to the last two books if Herbert did not drastically change his writing style.