The political allegories in the Oz books have possibly been overstated, although within the series there's plenty of social commentary (someone like /u/LibraryLass might be able to tackle Henry Littlefield's Parable of Populism better than I - it came out in the 1960s). One of the more interesting allegorical elements, though, is Baum's use of Theosophical imagery. Ideas from Western Occultism are fairly striking once you start looking for them, from the first book onward.

The influence of Theosophy on Baum is alluded to in The Annotated Wizard of Oz (edited by Baum biographer Michael Patrick Hearn), and has been examined by John Alego in "A Notable Theosophist: L. Frank Baum" and "Oz and Kansas: A Theosophical Quest".

The series has allusions to everything from astral projection to Akashic records and alchemical weddings, but one of the most obvious bits of occultism can be found in the first book, which is built around elemental symbolism. Unlike the movie, in the book, the Wizard appears to the four travelers in four different guises (a beast, a lovely lady, a ball of fire, a giant head), and the Land of Oz is divided into four countries each linked with a color... the heroes have four goals, linked to intellect, compassion, bravery, and domestic life... though they go on a quest, their real success depends on tearing away a veil disguising the true nature of things.... It's all pretty familiar stuff, if you've ever, say, looked at a deck of tarot cards or flipped through any other system of elemental correspondences.

This isn't to say Baum was writing an occult manual - it seems likely he was just playing around with these ideas because he found them interesting and thought kids might too. There are non-occult philosophical concepts in the books as well; The Tin Woodman is basically a walking, talking Ship of Theseus/grandfather's axe, for instance.

However, as editor of the Aberdeen Saturday Pioneer, Baum did write one editorial introducing readers to Theosophy (as quoted by Alego):

Amongst the various sects so numerous in America today who find their fundamental basis in occultism, the Theosophist[s] stand pre-eminent both in intelligence and point of numbers.

The recent erection of their new temple in New York City has called forth the curiosity of the many, the uneasiness of the few. Theosophy is not a religion. Its followers are simply “searchers after Truth.” Not for the ignorant are the tenets they hold, neither for the worldly in any sense. Enrolled within their ranks are some of the grandest intellects of the Eastern and Western worlds.

Purity in all things, even to asceticism is absolutely required to fit them to enter the avenues of knowledge, and the only inducement they offer to neophytes is the privilege of “searching for the Truth” in their company.

... and another about popular authors of the day (like Edward Bulwer-Lytton and H Rider Haggard) using occult themes in their bestsellers:

Books of this character are eagerly bought and read by the people, both in Europe and America. It shows the innate longing in our natures to unravel the mysterious: to seek for some explanation, however fictitious, of the unexplainable in nature and in our daily existence. ... The appetite of our age for occultism demands to be satisfied, and while with the mediocrity of people it will result in mere sensationalism, it will lead in many to higher and nobler and bolder thought; and who can tell what mysteries these braver and abler intellects may not unravel in future ages?

So the idea of taking these ideas and building stories around them was definitely something Baum was already thinking about in the 1890s - the first Oz book was published in 1900.