Of course people should study the relationship between Chinese philosophical and spiritual culture to martial arts, but they should remain grounded in reality and not "become possessed by a demon" (I mean they shouldn't get carried away in mysticism).
At the very least, if you do internal martial arts, you should understand Taiji, the five elements, and the bagua diagram. On a deeper level, when you interrogate the classics in their original language, some of them are very deeply connected to Daoism. Understanding how Daoism understands the structure of the mind can really help you make progress in life in general, I personally apply these concepts to every activity I do, not just martial arts and meditation.
On the other hand, if you want to go deeply into the religious beliefs of Daoism, you should be careful that the person who teaches you is a sensible person and not a lunatic, of which there are many. There is also huge wisdom in the more devotional aspects of Daoism, as well as Confucianism, Buddhism, and many other types of Chinese culture. On a personal note, studying these things has allowed me to make huge progress in my personal life, become much more peaceful, happy, and judge other people less than before.