What would have been necessary for a belief system such as Orphism to become a major religious sect in the world? Or, for that matter, something along the lines of Pythagoreanism or the Eleusinian Mysteries?
Too Greco-centric.
Being an ethnic religion didn't stop Judaism from being considered one of today's major religions.
Yes, but it's still a religion that transcends mere "ethnicity" by being an monotheistic religion having an all powerful being who is the supreme force of the world. The problem with Orphism is that it is too strongly rooted in Greek mythology, with the Orpheus conneciton being the main driving point.Being an ethnic religion didn't stop Judaism from being considered one of today's major religions.