Is there religious philosophy behind homeopathy and acupuncture?

Yes. Some Eastern religions like Taoism or Chinese folk religions discuss something call the Chi, which is the term for one's spiritual life energy. When Chi is out of whack, through stress and/or negative thoughts, certain treatments can bring it back into alignment and harmony, thus improving health and relieving pain.

only if the individual attributes one to it. On their own, neither is rooted in religion.
RN
Acupunture is part of the chinese way of life,the tao.
Not religious.
Homeopathy,no.
Homeopathy is based on the energy of the plant and only using a very small amount of the molecules of the plant to create the desired healing. Acupuncture is the use of needles in very precise point (mainly nerve centers) to create the desired changes or to heal certain things.
homeopathic cures have been around a lot longer than religions have
Some of the principles of acupuncture are rooted in Chinese philosphy. The meridians and flow of qi are functions of mysticism, but may be rooted in empirical observation.

Homeopathy is rooted in empirical observations of self administration.