Extract from Orpheus and Greek Religion, by Prof. W.K.C. Guthrie, first published 1935, text from the 2nd revised edition, 1952. p.196:
. . . the doctrine of transmigration . . .The reasoning was this. If the soul of a man may be reborn in a beast, and rise again from beast to man, it follows that soul is one, and all life akin. Hence the most important Orphic commandment . . . to abstain from meat, since all meat-eating is virtually cannibalism. . . .
[quoting Plato] 'Men abstained from flesh on the grounds that it was impious to eat it or to stain the altars of the gods with blood.' According to the words which Aristophanes puts into the mough of Aeschylus in the Frogs, Orpheus was famous for two things - he revealed the ways of initiation, and he taught men to abstain from killing. From the words of Aristophanes, it almost looks as if instead of saying at the beginning of this paragraph that the two things necessary for salvation were initiation and an Orphic life, we might have said simply initiation and a meatless diet. Again in the Hippolytus of Euripedes the taunt of Theseus at his son, now turned Orphic and bookworm, concerns itself with the 'meatless fodder' in which he glories since he 'has Orpheus for his Lord'. Empedokles, whose eachatology we have already seen reason to regard as identical wioth the Orphic, shows himself again thoroughly Orphic when he cries, 'Will ye not cease from killing?' Like Plato's speaker he looks back to a golden age in the past before such crimes were thought of, when . . . 'with the unholy slaughter of bulls was no altar wet. Nay this was held the height of pollution among men, to take away and devour noble limbs.' . . .
Both Plato and Empedokles refer to the age of innocence, before the sin of meat-eating was known among men, as having actually existed in past times. . . and made immortal to them by the poetry of Hesiod.
Extract from The Penguin History of Greece by A.R.Burn, © 1969-85:
Orpheus first appears in Greek art and literature about 540 [BC]. . . . From the first he was associated with the . . . discontinuance of human sacrifice. . . . People with a sense of sin resorted to self-employed practitioners called 'Orphic initiators'. . . . Certainly they did not preach 'pay me and do as you like'; on the contrary, the severer Orphic doctrines taught (not always consistently as there was no Orphic church) respect for all life, with its corollary, vegetarianism, and sexual abstinence. The movement . . . remained . . . far into Christian times.
[Note: the author of the above book is not at all sympathetic to vegetarianism, though even he has to acknowledge it. However it is a useful introduction to the general history of the era - ed.]