I am not going to claim to have all the answers in relation to whether or not acupuncture is in accordance with or against one's religious beliefs. That's not for me to judge. If someone were to tell me that they believed it went against their religion, I would have to respect that. My sense is that unless someone rejects any and all medical interventions as being counter to their faith, I don't see there being an issue with what acupuncture has to offer them.
Now, irrespective of the religion conversation, I get that acupuncture is a little different. The concepts at its core such as qi are not things that the typical American is going to quite grasp (after 3+ years of study, I have difficulty completely grasping the concepts myself). And that's ok.
Two questions/counterpoints to consider:
Dogs, cats, and horses are all often treated with acupuncture. Do animals need to believe in it for it to work for them? Clinical experience leads me to believe that they do not (and that it can be effective treatment).
Does a person have to believe in or understand how taking an aspirin makes their headache go away? How an antihistamine helps their breathing?
I hope this answer has been helpful.