I'm not sure if I'm getting where you are aiming at.
For instance, the armbands Muay Thai fighters wear are talismans full of magical powers (or at least they believed so). Is this kind of superstitious belief what would you consider integration of martial arts and spirituality/religion or are you asking about a different kind of integration?
the Muay Thai armbands is a good example. or the one that Ellis mentioned about Toda-ha Buko-ryu, where it served some technical aspect of the martial practice.