I think we should spend a significant amount of time defining “non-theistic” if we are to present Buddhism as non-theistic to the readers. For most people, I presume, a religion which posits the existence of supernatural creatures which have some degree of control over alternate realms and which can (according to some texts) even interact with this one is definitely theistic.
Second, you call the Buddha (I’m assuming you mean Gautama Buddha) a “mortal human being by all accounts”. This is quite puzzling considering that the Buddha is described as having multiple supernatural powers, and on one occasion travels into Brahma god’s realm to lecture him. (Brahma-Nimantanika Sutta, also a part of Pali Canon, mind you)
Third, you describe Buddhism as practically doctrine-less, in the sense that there are no specific beliefs which one must hold to attain salvation. This is a particularly cleverly-worded sentence, considering that beliefs are not the only thing Buddhism is about, and in fact much more emphasis, enlightenment-wise, is put on practice. To this end, we can certainly say that there are ways believed to be much more efficient and reliable, like leading a monastic life or having an enlightened teacher - Sariputta leaped one degree closer to sainthood by listening to one verse from Assaji. (Upatissa-pasine from Vinaya Pitaka, also part of the Pali Canon) There’s even sort of a road-map for achieving enlightenment in Theravada, in the form of four stages of enlightenment. Similarly, there’s definitely things one is absolutely forbidden from doing certain things (matricide, patricide, attempting to kill an Arhat, injuring a Buddha, creating a schism in a monastic community), and doing any of these will inevitably result in being reborn in Avici (a hell of constant torment). On this ground, I think that traditional Buddhist ethics is in places much closer to traditional Christian ethics, in the sense of carrot-and-stick treatment of behaviour.
The conclusion, for me, is that there is a multitude of ways one can interpret the Buddhist texts, and history shows that this has happened. This isn’t surprising, considering that Buddhism shares with Hinduism the approach of being all-encompassing and pluralistic. The readers, some of which might have a rosy view of the religion, should also be acquainted with its less pleasant dogmas present in some of its schools.
I think it’s a bit hyperbolic to say that being uncertain about including a discussion of a very broad subject in a short section is “tacitly supporting” any dominance.
I’m not an expert on Taoism, but there are metaphysical claims made in some of its texts, and it features some esotericism (alchemy and such), depending on which source you consult. As far as I know, there is no central authority, so it’s not really possible to nail anything down as “definitely Taoist”.