The following states allow non-veterinarians to practice equine dentistry.
AZ AR CT FL IL LA ME MD MN OK SC TN UT VT VA
In 2014 the specialty practice of equine dentistry with specialty board certification via the DVM/VMD route was established. Board certified equine dentists are still quite rare. I was able to find only 27 such trained specialists listed as practicing in the USA.
I do not know the specific pathway to achieve this status other than it requires 3 to 6 years of training after veterinary school. This makes sense because board certification in human oral surgery also requires a minimum of 4 years of post-dental school residency training, so paths to board certification are at least comparable in time.
My point is that people practicing as equine dentists equine range widely in background, education, training, and experience.