My research program is based around a technique that I blew off as pseudoscience as a grad student!
In my case, I thought the technique, transcranial electrical stimulation, was unlikely to meaningfully affect brain activity, but a funding agency really wanted to know for sure. I figured that I could do some really careful experiments, drive a stake through the heart of a silly idea, and then move on. In fact, I was most interested in the control conditions, which would test out some other (safer, more conventional) ideas I wanted to work on. However, once the data started coming it, it became clear that it did do something! My initial skepticism wasn't totally unwarranted: the effects were different than some groups had claimed and I certainly wouldn't want to co-sign everything the field has done, some of which still seems dubious to me. Still, digging into how it acts has been a lot of fun. Beyond the science itself, helping nudge (in my own, small way) clinical work onto the "right" path has also been rewarding.
Your advisor may have something similar in mind. It could be an "adversarial collaboration": he and his new collaborators genuinely want to know whether the putative treatment works, and the best way to determine that (especially for skeptics like yourself), is to tackle it with the high standards of scientific rigor that you say your advisor is known for. It may be an indirect route towards something more aligned to his usual research. He may doubt that their green tea extract (or whatever) has any special properties, but the control data collected during these experiments might support his long-standing interest in placebo effects or adenosine receptors[1]. Of course, he could also suspect that there's something to it. "Natural products" have inspired—and indeed, are the actual physical source—of many conventional treatments. Treating pain with flowers sounds preposterous, but opioids like codeine and morphine are still among our best options (and biggest problems). Moreover, the natural source is often the best or only way of producing it. Total synthesis of morphine is possible but so inefficient that most of it is still derived from poppy plants [2].
Thus, consider having a friendly, low-key conversation with your advisor about it. What piqued his interest in this field? What is he hoping to do? How does this fit in with the rest of his research interests? It may be useful and edifying to see how a senior person develops a new line of research. Perhaps he will even persuade you that it's not as crazy as it seems!
Still not convinced? The good news is that it doesn't really matter much to you, personally. You're wrapping up your PhD and are presumably more comfortable with your own thesis topic. You can politely decline new projects in the interests of finishing up and submitting. In fact, you should probably do this anyway! If you are worried about future letters, you hopefully have a thesis committee who can also vouch for you. You should certainly firm up your relationship with them and this is also a good idea anyway too: many fellowships need multiple letters!
Good luck with the rest of your work!
[1] A target of caffeine.
[2] I think. I am neither a licit nor illicit pharmacologist.