https://sciencebasedmedicine.org/reference/chiropractic/
https://pubmed.ncbi.nlm.nih.gov/11045895/
That is not to say we don't definitively know they do not work. We just dont know if they do anything or not. There is promising preliminary research but a lot of that research is coming out of a community that appears prone to some serious motivated reasoning. And there is a small cultural movement brewing that seeks to promote them despite our current ignorance. Proponents have made a mad dash to dump them into alt med toolbox to sit alongside acupuncture, cupping, ear candling, essential oils, etc.
Edit: Don't get me wrong. I really hope these do work as the current standards of care for most mental illness are terribly flawed. Lithium for example is amazing but it has horrible side effects, destroys your organs and for many eventually stops working. Abilify has saved a lot of people's lives but when you're on it, a lot of times you just fucking want to die. It would be great to move beyond SSRIs, mood stabilizers and antipsychotics.