Let others do Homeopathy and Iridology. Many societies have split health care into a scientific system and a non-scientific alternative. Perhaps we will follow the same path. As Idealists we wish first to do no harm, and secondly to server the patient's health. Homeopathic therapies are certainly unlikely to do direct harm, though herbal remedies certainly might.
Indirect harm is likely, however.
A patient may delay effective therapy while pursuing harmless but ineffective remedies. Patients who seek out a physician for medicine based on science may later feel betrayed by therapies based on non-scientific principles. When we say we serve the patient's health, we mean our first duty is not to the patient's stated wishes, but rather to their health as we can best understand it. An accountant cannot ethically falsify tax returns, a lawyer cannot ethically advise on breaking the law, a physician should not act against a patient's health even if they ask it of us. Even if a patient is convinced that chronic antibiotics can treat their hypertension, most physicians would not choose this therapy.