How exactly do you practice SBM? I find this difficult to believe, since as far as I'm aware there are no science based medical schools, no science based clinical guidelines, no research into the efficacy of science based treatments, etc. As far as I can tell it's just a poorly defined idea that isn't even logically coherent enough to have any real world practitioners.
For whatever flaws may exist with naturopathy, at least it's a real thing with legitimate practitioners.
edit: Also, your assertion that Dr. Auer advertises himself as a homeopathic practitioner isn't even accurate. His actual bio states, "Dr. Auer is continuously furthering his education and understanding of the body through post-doctorate courses and various seminars ranging from functional medicine, functional endocrinology, natural hormone balancing, holistic nutrition, homeopathy, herbology, chiropractic neurology, and various chiropractic and soft tissue techniques."
In other words, he is saying that he has studied homeopathy to some extent. Which if you haven't done, you're probably not a very good doctor.