‘Men who eat bread’ isn’t a restrictive clause, ‘she avoided men who eat bread (but not other men).’ In the original language it’s an attributive epithet: ‘she avoided men, and BTW men eat bread.’

Epithets of this kind are a little misleadingly called formulaic in early Greek hexameter: misleading because it isn’t a matter of typical language controlling the poetry. It’s better to think of ‘formulas’ as tools that the poet has at their disposal.

‘Bread-eating men’ is a standard epithet in early Greek poetry. It appears 3 times in the Odyssey (1.349, 6.8, 13.261), once in the Hymns (Hymn to Apollo 458), 3 times in the entirely extant Hesiodic poems (Theogony 512, Works and days 82, Shield 29), and twice in the fragments of the Catalogue of Women (fragments 73.5 and 211.12 ed. Merkelbach & West — this papyrus is fr. 73).

The extant text runs
[ ἀνθρώπων ἀ]παναίνετο φῦλον ὁμιλ[εῖν]
[ἀνδρῶν (ἐλπομένη?) φεύγ]ειν γάμον ἀλφηστάων

she shunned associating with the tribe [of humans]
[(hoping? wanting?) to es]cape marriage with bread-eating [men]
Square brackets indicate the edge of the papyrus. There’s no doubt about supplementing ἀνδρῶν in the second line, because it is a formula, and ἀνδρῶν means ‘men’ — that’s the ‘bread-eating men’. But in ye olden days some people liked to translate the gender-neutral ἀνθρώπων as ‘men’ too — but doing so here would produce a repetition: ‘she shunned men, hoping to escape marriage with men’. I imagine, though I can’t be sure, that ‘rejected her equals’ is the translator’s way of avoiding that repetition.

As for the meaning of ‘bread-eating’, literally it’s ‘barley-eating’. The usual way of interpreting it is as a way of referring to people who have agriculture — as distinct from animals (and perhaps hunter-gatherers).

Older commentators opt firmly for the meaning ‘non-hunter-gatherers’. But they also habitually treat ‘hunter-gatherers’ as synonymous with ‘savage’ and ‘raw-meat-eating’, so all that tells me is that we urgently need new commentaries.