It's not a "new Hippocratic oath," it's just an oath. Schools have been using student-written oaths for quite some time. They are not legally binding. Nobody is forcing you to say it out loud, cross your heart and hope to die at the white coat ceremony or at graduation. They also use other oaths such as the Declaration of Geneva pretty frequently. If you actually read the Hippocratic oath, it's pretty dated and irrelevant to medicine today, and there are certainly aspects of that oath that many folks disagree with...some schools use it anyway. If this is something that bothers you and you attend a school that has a student-written oath, I'd encourage you to join the oath-writing committee to make your voice heard.
Also, honoring indigenous ways of healing does not mean that you are necessarily prescribing them. We can honor and respect our patients' cultural beliefs related to health and healthcare and incorporate them into an evidence-based plan when appropriate. As long as those indigenous ways of healing are not actively harmful from a medical perspective and used in conjunction with modern medicine in a way that is consistent with the patient's goals and values, it can actually be a huge help in terms of spiritual/emotional healing and support for the patient, and help build a trusting, understanding, and therapeutic physician-patient relationship.
I have a patient who had an A1c of 15% when she received her diagnosis of diabetes. She was terrified of starting any new medications because of worries about side effects. She instead wanted to take some concoction of celery juice, turmeric, cinnamon, raw honey, and some other stuff daily and focus on dietary changes. Now to the best of my knowledge this is not necessarily an indigenous/cultural remedy of any sort, but she does have a cultural background that has a historically challenging relationship with the healthcare field that I think makes her more likely to seek alternative methods of managing her care. I said great, lets talk about some dietary changes, you can try your juice thing and see how it goes - and I continued to educate her at every visit about diabetes management and what role medications play. Because I was open to at least working with her on her point of view, she ultimately let me start her on some metformin and a statin, and followed with me consistently for appropriate preventive care and review of her blood sugar logs so we could work on lifestyle changes together. Her A1c today is 6.5% on half of the max dose of metformin and her juice thing. I don't think the juice brought her A1c down by 9%, and frankly probably neither did the metformin...but I do think my being respectful and understanding of what made sense to her - honoring her ways of healing - helped us build a relationship that facilitated the lifestyle changes that probably made the actual difference and keeps her coming back to me for appropriate care.