G. de Purucker in his introduction of the Esoteric Tradition (1940) explains the meaning of theosophy being non-dogmatic. It demonstrates, that the modern theosophists rejected belief in (and describes the reason the theosophist does not engage in) worshiping the gods and the initiated.
Dogma in The Esoteric Tradition by G. de Purucker
“The word dogma comes from the Greek verb dokein, “to seem to be,” “to appear to be.” A dogma, therefore, was something which appeared to be a truth: an opinion about truth, and hence was frequently employed in certain Greek states as signifying the decision, the considered opinion, and therefore the final vote arrived at in a state council or assembly. It was only in later times that the word dogma acquired the meaning which it now has: a doctrine based upon the declaration of an ecumenical council, or perhaps of some other widely recognized churchly authority. In this modern sense of the word, then, it is obvious that theosophy is wholly non-dogmatic: it has no teaching, no doctrine, imposed as divinely authoritative upon its adherents, or derivative from some individual, or body of individuals, claiming authority to declare that this or that teaching or doctrine is truth, and that it must be accepted and believed in by those who wish to be theosophists. The theosophist, however, claims that the teachings have been tested by adepts and great initiates through unnumbered centuries, this testing being a comparison with spiritual nature herself, which is the ultimate tribunal of proof. Each new generation of these seers tests the accumulated knowledge of its predecessors, and thus proves it anew; so that as time goes on, there is a continual perfecting of details.
Seers means those who see: who have so largely brought forth into activity the spiritual faculties and powers in themselves that their inner spiritual nature can at will penetrate deep into the arcana of the universe, go behind the veils of the outer seeming, and thus seeing, can interpret with accuracy and fidelity. Hence, their doctrines are consistent and coherent throughout.
From time to time this Brotherhood of (…) evolved men gives forth [deliberate and concerted efforts?] to the world new-old vistas into nature’s secrets, stimulating man’s ethical instincts, arousing his latent intellectual powers, in short, bringing about the constant albeit silent evolutionary urge forward to greater and nobler heights of human achievement. The theosophical student finds it within the compass of possibility to examine these archaic doctrines and in his turn to test them with his own capacities, however limited these may be; and thus it is that time, in its unfolding of things out of the womb of destiny, brings forth to the faithful inquirer abundant proofs, checked and examined at each step by himself, that these doctrines are truths based on universal nature — nature spiritual and material with all the countless hierarchical ranges between.
Probably not in historical times has there been such a widespread awakening in religious feeling and in general religious interests as exists today; but no longer do men quibble and fight as much over mere questions of form, theological or ecclesiastical, nor over hairsplitting definitions of words involving doctrines, as they did during the Middle Ages and after. Rather is the feeling today that there is a concealed but not unsolvable mystery behind the veil of the outward seeming of nature, and that the only way by which to acquire this reality is to penetrate into the temple of Truth oneself — into the very heart of the Invisible. All men are able to see if they will but fit themselves for the seeing, and no man with this conviction in his heart will ever declare dogmatically: “I am the prophet of truth!”