I can understand why someone who isn't religious wouldn't feel any need at all to embrace a philosophy that has some churchy aspects -- such as Zen Buddhism and Taoism.
However, I enjoy reading books in both genres, and am heavy into Tai Chi, which expresses Taoist principles in movment.
It seems to me, along with others much more knowledgeable about Eastern philosophy than I am, that Zen minus Buddhism equals Taoism.
(More or less, at least. We're not talking mathematical precision here.)
Buddhism adds in a bunch of religiosity to Zen, which would be more closely related to Taoism if it didn't have all those revered masters uttering supposedly profound commentaries on the sutras, etc. etc.
Hans-Georg Moeller does a nice job of describing why Taoism/Daoism is less annoyingly religious than Zen in his book, "Daoism Explained."
Daoism is much more into the body.
Daoist philosophy takes the body very seriously. Although Buddhism, especially in its early Indian forms, also cares about the body and even includes yogic practices, it focuses much more on the mind and its "spirituality."
...Early Daoism did not react to a Buddhist philosophical background, and it did not develop into a philosophical discourse in which consciousness was a central issue.
...In Daoism, the "mind' is more or less understood in bodily terms. It is integrated into the functioning of the body and is not a separate force or constructive power. I believe that this constitutes one of the main differences between early Daoist philosophy and later Chan [Zen] Buddhism.
Daoism more strongly affirms the reality of the real.
Daoist philosophy, as I hoped to show, generally affirms the world of "presence" (you), that is all the "ten thousand things," life and death, even action and speech. The nonpresence (wu) in the midst of presence -- the emptiness that is neither dead nor alive and neither acts nor speaks -- does not expose any "relativity" of the present. Daoist emptiness and nonpresence do not diminish but rather confirm the authenticity of the present.
In comparison with Daoism, Chan has a more ambiguous concept of the reality of the real. Like Daoism, Chan also affirms the autheticity of the here and now, but it also affirms its inauthenticity. The Chan Buddhist ambivalence in regard to the reality of the real is evident in its well-known "rule of three." A mountain is a mountain. A mountain is not a mountain. A mountain is a mountain.
...In the end, the inauthentic is also accepted as authentic, and this is represented by the final statement that again sees the mountain as the mountain. This third level of reality is not to be equated with the first; it is more complex and has integrated or "superceded" its own negation.
...Ancient pre-Buddhist Daoism affirms the full reality of the real.
Daoism has a less religious institutional character.
Even though both Laozi and Zhuangzi are portrayed as masters who answer the questions of disciples, the sources do not indicate that they were revered as religious leaders by "monks." Even though Chan Buddhists were extremely critical of Buddhist religious institutions, many of them lived in monasteries.
...The more religious character of Chan Buddhism is also demonstrated by the nature of its most important writings. The Laozi is a colllection of philosophical poetry, and the Zhuangzi is a book that includes allegories, dialogues, and short philosophical treatises.
In contrast, Chan Buddhist scriptures are often sermonlike speeches (like the famous "Sutra of the Sixth Patriarch") or records of the sayings and deeds of important priests (the so-called yulu) as noted down by the monks in the monasteries.
Naturally l like both Zen and Taoism a whole lot better, than, say, fundamentalist Catholicism (is there any other kind?).
But when I need some non-religious inspiration, more and more I tend to turn to Taoist writings of the philosophical variety. Taoism does have its own religious, supernatural side, which doesn't appeal to me. I enjoy the lighter, looser, more laughable vibe of Taoism, as compared to Zen.
Zen Buddhism also enjoys a joke, but only if one's sense of humor comports with what a Zen master dude considers is funny. If you laugh at the wrong time, or in the wrong way, he'll hit you over the head with a stick.
Philosophical Taoism doesn't have that sort of hierarchical, patriarchal stuff. Everybody is just wandering on their own path in the misty mountains, enjoying nature, doing their own thing.