A Navaho sand painting ritual for a sick child is a mystery – we literally cannot read the signs nor subscribe to the belief, let alone the science, that she can be made better this way.
Does here "let alone the science" want to say "as we cannot understand these sand paintings and science cannot understand them either"?
The usage of "let alone the science" is used to say that, in addition to the inability to subscribe to the belief (that is, to follow it and believe it), there is also an inability to subscribe to the science (again, to follow and believe it). The phrase "let alone" refers back to the previous phrase of "we ... cannot ... subscribe to the belief" and, without the previous statement it is rendered confusing and incomprehensible. It is dependant on the previous statement.
As for your question "Does here 'let alone the science' want to say 'as we can not understand these sand paintings science can not understand them either'?", the answer is no. This sentence is actually saying something along the lines of "we cannot read the signs nor can we follow the beliefs and science behind the idea that she can be made better this way."
We can revise the sentence in question—
A Navaho sand painting ritual for a sick child is a mystery – we literally cannot read the signs nor subscribe to the belief, let alone the science, that she can be made better this way.
—to give it a more systematic presentation that may make the sense of of the words "let alone" in the original easier to comprehend:
To people outside traditional Navaho culture, the Navaho sand painting ritual for treating a sick child is a mystery. It involves symbolic or occult signs that outsiders can't read, and it relies on a belief in its efficacy that outsiders don't have. And if the ritual possesses scientific underpinnings as well as shamanistic ones, outsiders have even less grasp of the science involved.
In other words, the author is saying "Let's set aside any inquiry into the scientific basis of this sand painting ritual because we can't begin to assess that until we've fully appreciated the ritualistic aspects—and we are utterly unequipped to do even that." We can't subscribe to the science of the ritual, because we can't subscribe to the belief in the ritual's efficacy, which is the prerequisite for subscribing to the science. Thus "let alone" here means something like "and far less."
By structuring the original sentence in this way, the author rhetorically disqualifies "us" from holding any valid opinion about the scientificness (or lack thereof) of the sand painting ritual. It's rather like saying that you can't even consider the scientific aspect of snake handling as a path to faith and righteousness in primitive Christian churches of the U.S. Upper South without first understanding the belief in and symbolic meaning of snake handling in those churches.
This is a more mechanical analysis of your quote. You ask:
Does here "let alone the science" want to say "as we cannot understand these sand paintings and science cannot understand them either"?
No. Here's why.
There are two idiomatic forms used together:
We apply the first, with
so the relevant part can be rewritten as "[we literally] cannot Y ...", or "[we literally] cannot subscribe to the belief, let alone the science ...".
We then apply the second idiomatic form above to this, with
to get "[we literally] cannot subscribe to the belief, and certainly cannot subscribe to the science, ...".
Putting this back into the context produces, as others have observed, the statement that the author cannot subscribe to the science that "she can be made better this way", not that science cannot understand the sand paintings.
