William James was a Theosophist (no religion higher than truth). Theosophy is another mystery school, like Masonry which preceded it (look into Leadbeater & Olcott, Blavatsky's handlers), and like Anthroposophy, which splintered from it in-turn. These schools seem to have been undertaking the syncretization of all world religions known at the time. Immediately after the fall of the Knights Templar, we get the Masons--mixing the Abrahamic with the Egyptian and Mithraic. Then, as the Hindu and Buddhist doctrines made their ways into western consciousness in the 19th c., these also had to be retconned into the mix, ergo Theosophy.

So, of course James would be one to write about such things, but he was standing on the shoulders of giants; a disclosure of received wisdom more than personal insight. And if you are interested in such things, the more recent mystery schools--Theosophy (Blavatsky), Anthroposophy (Steiner), Perennialism (Guenon), Esalen (Huxley, "The Perennial Philosophy")--are all good places to start.