I'm genuinely asking. My understanding is that we also accept those axioms.
"Science adjusts it views based on what's observed, faith is the denial of observation so that belief can be preserved"
The main axiom of panpsychism, if I understand correctly, is that all or most objects of reality have a mind. Now, as an axiom in itself it is pretty imprecise and not self-evident at all, as it depends on the definition of "mind". Also, it doesn't seem to create testable or useful theories out of that axiom.
However, from what I recall, they don't present the ideas in the book as facts or established theories like your critique seems to imply. They make it very clear that this is uncharted territory and that there is a lot of science to be done. In fact I think one of the main purposes of the book was to convince the reader that there is in fact tangible research to be done in the subject, and questions worth asking.
A large proportion of the book is indeed spent convincing the reader that panpsychism is a worthy theory, yes. And despite their lack of empirical data (which has proven hard to collect in this area), they make logically sound arguments that the theory is at least worth further consideration.
This is how many scientific theories start, as hypotheses that seem logically sound but lack specific empirical evidence. These hypotheses then guide how we design our experiments. The book argues that panpsychism is a worthy hypothesis, and it does not do so by referencing any woo or pseudoscience.