Since the origins of yoga are directly spiritual and even in the origins it is said you cannot separate the spiritual aspect (Hinduism) from yoga, i don't see how any yoga could be seen as acceptable. Eastern belief and elements are permeating the US due to it's subjective morality and subjective truth. DIY religion where you can make up the rules as you go. No deep spiritual meaning there. As a result eastern religious practices have become commonplace. Essentially engaging in yoga is engaging in a practice that was formed specifically for mystic spirituality.
Tai chi is a Chinese philosophy development that may be less purposefully spiritual, but the ancient eastern philosophies seemed to tie directly into everything.
Roots of Tai Chi
"The philosophical term Tai Chi was first described in two Chinese Taoism books; Book of Change and Tao De Ching written around the 2nd millennium B.C.
After researching and observing natural phenomena, philosophers such as Lao Tze, and Chuan Tze arrived at the conclusion that everything in the universe was cyclical. Tao is translated as the "Path", or the "Road".
The Path encompasses living quietly, simply, disciplined and in tune with the cycles of nature in order to achieve harmonic life. The Taoism philosophy upholds two fundamental principal notions called Ying and Yang. Ying and Yang exist and move in opposite directions within a shared circular boundary. Because they move as opposites, they are able to achieve a natural balance. They compliment each other to achieve natural harmony. Thus the classic symbol ☯ was formed. The ultimate effect of this harmony, according to Taoism, is one's physical health (Yang) and spiritual well-being (Ying)."
http://www.octaichi.com/tai-chi-history-and-benefits/roots-of-tai-chi.html
"Physically, the body moves to a specific motion in order to compel the flow of internal energy. This energy is called "Chi" and its purpose is twofold.
Primarily, Chi is our life-energy, the source of our internal thought, control and focus. Secondly, Chi also acts as the energy with which we self-heal. The focused circulation of Chi relaxes the mind and alleviates the stress of our body. Improved blood circulation, balance and improved mobility are but a few of the visible results of increased Chi strength."
http://www.octaichi.com/tai-chi-history-and-benefits/what-is-tai-chi.html