Interesting point Chris.
It would in fact be a good exercise for people to inspect what their agenda is rather than say they don't have one. Maybe some have too much significance on the word.
I also note you mention shamanic practices. Now that's getting more spiritual I must say. It could also equate quite well with Ueshiba's type of Shinto.
In fact my partner in crime Aikido wise, who has trained with me for over thirty years is a qualified shamanic osteopath. All fascinating stuff. We ended up teaching those people too for a year.
Another interesting point you make about the spiritual folk who then started practicing tai chi. I find this type of situation often to be true where spiritual are quite divorced from the 'body' so to speak or to be more blatant from the reality of what they have learned.
I find it in those who do reiki or even forms of ki atsu, yoga, meditations of different kinds, even tai chi etc. Not all, but many. I tend to break up religions and spiritual practices now into two camps. Let's say religious philosophy and rites and rituals as one camp and religious practice as the other. Same for spiritual pursuits.
It has been my experience to note that most religions are male dominated and ruled. Thus, a male mindset and attitudes predominate. Even the idea of the cross was not the original Christian sign. It was a fish. Later, once Christians began joining the Roman military, crosses appeared, likely as a sublime influence from Mithras Cult that was popular in military (Male only) ranks. And they loved blood letting on bulls....
I literally danced when one female asked Ken Wilbur, "What would Buddhism be like if the Buddha was female?" He first says it would probably not be consumed with quietly staring at walls, extreme body molification and developing equanimity. Instead, he drew from the female Christian mystics saying they would likely be kissing the puss-filled degenerating bodies of lepers, searching for the ultimate in selfless love. Well, that is definitely being in the body.
Another good resource:
Therevadic Aesthetic Aloofness OR Non-dual Suchness? A good lecture.
In the world today, a feminine energy is covering us like a tsunami. Andrew Harvey's Book "Return of the Mother" covers this event very well from Jesus to Ramakrishna, and Aurobindo.