The claim that Euripides was “a torchbearer in the rites of Apollo Zosterius” comes, like many other biographical claims, from a short Life or Vita that was prefixed to the Byzantine manuscripts of his plays. Modern scholars are skeptical about the reliability of this work. Mary Lefkowitz wrote:
Close analysis will show that virtually all the information in the Vita derives from comedy or Euripides’ own dramas; that anecdotes endow the poet with both heroic capabilities and degrading weaknesses; and that over time these weaknesses gradually receive more emphasis, in order to make the poet’s achievement seem more comprehensible and accessible.
Mary R. Lefkowitz (1979). ‘The Euripides Vita’. In Greek, Roman, and Byzantine Studies 20:2, p. 188.
Here’s an example of a detail in the Life that is clearly derived from a fictional source:
They also say that women lay in ambush for him at the Thesmophoria because of his criticisms of them in his poetry. They wanted to destroy him, but they spared him first because of the Muses and then because he promised never again to say anything bad about them.
Life of Euripides. In Lefkowitz, p. 192.
This is just a summary of the plot of Aristophanes’ play Thesmophoriazusae, which is a comic satire on Euripides, not a documentary about him!
Another line of evidence for the unreliability of the Life comes from indications that other writers disputed the claims therein. For example, the Life begins:
Euripides the poet was the son of Mnesarchides, a storekeeper, and of Cleito, a vegetable-seller.
Life of Euripides. In Lefkowitz, p. 189.
but the Suda says that some of this was refuted by Philochorus, a 3rd century BCE historian:
It isn’t true that his mother was a vegetable-seller, for it happens that both his parents were well-born, as Philochorus demonstrates.
Suda, entry for ‘Euripides’. In Ludolf Kuster, ed. (1705). Suidae Lexicon, volume 1, p. 906. English translation by Lefkowitz, p. 189.
Like the Thesmophoria claim, the vegetable-seller claim seems to be derived from the lampoons of Aristophanes, for example, in Acharnians 478, where Dicaeopolis insults Euripides by asking for “the chervil your mother left you in her will”. It seems plausible that there was some underlying truth to this, otherwise the lampoon would not have stung. But again the point is that the Life has no independent evidence.
The claim that Euripides was an adherent of the cult of Apollo is not one of the claims with a clear fictional source, so it may, for all we know, be true:
Only two incidents in the Vita sound unique and therefore possibly of historical significance. But here again we may suspect they found their origin in some literary source. Both are favorable to the poet. (1) Euripides acted as a torchbearer in the rites of Apollo at Cape Zoster
Lefkowitz, pp. 197–198.
Howwever, it would not be surprising if this detail came from a work that is now lost (since we only have eighteen or nineteen of Euripides’ ninety-plus plays and eleven of Aristophanes’ forty). Lefkowitz suggests a motivation for doing so and offers a parallel:
Was a passage from some play now lost cited to counter charges of Euripides’ atheism, in the way that Satyrus describes how Euripides “admirably incites the youth to valor and courage?”†
Lefkowitz, p. 198.
† Satyrus (3rd century BCE). Life of Euripides, fragment 39, column IV. In A. S. Hunt, ed. (1912). The Oxyrhynchus Papyri IX, pp. 124–182. London. Online at livingpoets.dur.ac.uk.
In summary, if Euripides really was an adherent of the cult of Apollo, the only information we have is the one sentence in the Life. But more likely, this is as fictional as some of the other biographical claims, such as the story that he wrote all his plays in a cave, and the story that he died by being torn to pieces by a pack of dogs.