I can’t help but wonder if we might substitute “osteophath” for “homeopath”; osteopaths are real doctors and all (although some allopaths would disagree). In general, the approach is to try to treat causes rather than symptoms - so that backache may not get you Oxycontin, but a spinal adjustment.
D.O.'s and M.D.'s don’t always share like minds, but they both prescribe drugs, do surgeries, and all that other stuff. Homeopaths can also be doctors (like, if they graduated from the American College of Homeopathy), and it’s not literally about treating with poison. From my understanding, a good example is the use of poison ivy to treat things like eczema, chicken pox, and other itchy afflictions. I can’t vouch for the science… not my field. But the fact that homeopathic approaches have been regulated in the US since 1838 gives at least bureaucratic acceptance.
Appeal to Antiquity and Appeal to Authority, two logical fallacies.
And I don’t know of any MDs these days who dismiss DOs just based on osteopathic training. Both types of schools rely on the scientific method and evidence-based medicine.
As for your claim of acceptance since 1838 in this country, you’re off by a century. Non-Regulation of homeopathy
So a homeopathic practitioner and legislator created the governmental recognition of and exemptions for homeopathy.