Ordinarily, there should be no problems.
My mother had great success with a Christian acupuncturist who has sadly retired, and she has not had the same level of pain relief from a spinal injury decades ago since that time about twelve years ago.
On the other hand, the same acupuncturist had no positive effect on me.
Now, acupuncture is based on traditional Chinese medicine, which is conceptually distantly related to Taoism and Confucianism and other folk beliefs, insofar as it believes in four elements and Qi, a flow of energy, but traditional Western medicine is likewise even today distantly related to ancient Greek philosophy in terms of the naming of specialities, the Hippocratic Oath, and the pioneering work of Greek and Roman and Arabic doctor-philosophers such as Hippocrates, Galen, Avicenna, and some more recent practitioners of Alchemy, the same mystical pseudoscience that features prominently in Taoism and neo-Gnostic occult heresies, notably the German Paracelsus who had the insight “the dose makes the poison.” Of course, Western medicine has moved on mostly from those ideas of the past debunked by science, such as the Four Humours and the Five Elements, except for Chiropractic medicine, which is mostly quackery (my mother was once seriously injured by a chiropractor and I have been advised by my doctors to not see them due to the specifics of the disease which afflicts me) whereas Traditional Chinese Medicine still holds to a similiar set of beliefs.
However, unlike many forms of alternative medicine, my understanding is that acupuncture has been shown to have some efficacy, and if it works its a great alternative to, for example, having to use opiods, which are becoming harder for chronic pain sufferers with legitimate prescriptions to obtain, not to mention victims of acute pain, and the terminally ill, with a national shortage affecting hydrocodone in particular, largely due to regulatory issues, despite the fact that there now exist effective computer-based prescription systems in every state that completely prevent doctor shopping, and the opioid epidemic now consists mainly of people dying from the abuse of illegally obtained fentanyl (the only legitimate uses for fentanyl are in the OR and in the care of the terminally ill; using fentanyl without being monitored by an anaesthesiologist is insane because it is hundreds of times more potent than even morphine, let alone painkillers like norco or percocet).
So by the way please pray for chronic pain sufferers who are experiencing diffficulty accessing lawfully prescribed medications. A year ago they were readily available at most pharmacies but in some areas are now hard to find even at CVS or Rite Aid or Walgreens, with the small independent pharmacies that often used to specialize in pain management now being completely unable to source them in many cases.