Unfortunately for you, the power of attorney for medical decisions would control. You would not be able to challenge the decisions made by your wife's appointee.
This comment is given for educational purposes only. No attorney-client relationship exists between us.
The agent under the Power of Attorney would be authorized to make decisions concerning your wife's care and treatment. Their authority as agent would trump yours as husband. Unfortunately, as you put it, your hands would be tied.
Bear in mind that the Power of Attorney likely springs to life upon your wife's inability to make these kinds of decisions for herself. Appointing an agent is a deeply personal act, and religious concerns can certainly play a role in the decision. I feel pretty certain that you have had a very open, honest and frank conversation with your wife regarding this. If not, it's a conversation worth having while your wife has the ability to express her desires and concerns.
This answer does not constitute legal advice. I am admitted to practice law in the State of Texas only, and make no attempt to opine on matters of law that are not relevant to Texas. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should never rely on this answer alone and nothing in these communications creates an attorney-client relationship.