Some might argue that 'church and state' should also be separated as much as 'personal principle and rules of practice'. Ethics change with time. Some argue its for the better and others for the worse.
My religious beliefs do not get the way of my personal practice. If they did, I would be inappropriately forcing my views and beliefs upon patients, and that is unethical. Freedom of religion allows us all the right to health care apart from anothers religious convictions. The other argument is that freedom of religion allows us to carry out our duties without being compromised by anothers lack of convictions. Basically than, if someone wants an abortion and a doc says that he will not perform it based on religious convictions, find another doc. If a pharmacy will not prescribe a drug based on the same values, find another pharmacy. Our freedom of religion provides both liberty to some and restrictions to others. We have to respect this fact and work around it in order to claim the same right of liberty.
Ethically, should a medic be forced to get their flu shot so that they will not get the flu. After all it is 'apparently' in the best interests of the patient. Or is it in the best interests of the service provider to control having masses of their employees off sick. Getting the flu shot may reduce your probability from getting the flu, yet does not stop the medic from being a carrier/reservoir of the virus. So what happens when we start in an occupation with the lack of stringent regulations for inoculations, and the regulations change mid career to offend your principles and values? Do you accept it and go with the flow? Resist it and buck the system? Or find another occupation because the regulations enforced offend your principles and religious values.
I have not so much provided an answers, just more questions and the potential for ethical debate and controversy.
I did get my flu shot this year because otherwise I would be forced to wear isolation equipment every time I did a medical call. If this was not the case I would not have gotten the shot as I do not care for the unknown long term effects of the drug.