Ἐὰν δέ τις Ἰουδαϊσμὸν ἑρμηνεύῃ ὑμῖν, μὴ ἀκούετε αὐτοῦ. ἄμεινον γάρ ἐστιν παρὰ ἀνδρὸς περιτομὴν ἔχοντος Χριστιανισμὸν ἀκούειν ἢ παρὰ ἀκροβύστου Ἰουδαϊσμὸν. ἐὰν δὲ ἀμφότεροι περὶ Ἰησοῦ Χριστοῦ μὴ λαλῶσιν, οὗτοι ἐμοἰ στῆλαί εἰσιν καὶ τάφοι νεκρῶν, ἐφ᾽ οἷς γέγραπται μόνον ὀνόματα ἀνθρώπων.
But if anyone expounds Judaism to you, do not listen to him. For it is better to hear about Christianity from a man who is circumcised than about Judaism from one who is not. But if either of them fails to speak about Jesus Christ, I look on them as tombstones and graves of the dead, upon which only the names of people are inscribed. (Holmes 2007: 240, 241)
I've encountered this passage before, which is a bit odd since I've never read any of the Apostolic Fathers (other than the Didache); perhaps Boyarin addressed Ign. Phld. 6.1 in Border Lines. But I think a few observations are possible here, especially on the strength of the discussion in my post, "Judaism and Christianity (Ign. Magn. 8–10)."
First, Ignatius appears to imagine the "anyone" [τις] who expounds Judaism as being a gentile. This, perhaps, isn't a necessary inference from the comparative statement, but it does seem to me that Ignatius exhorts the Philadelphians to shun a particular content (Ἰουδαϊσμός) rather than a certain ethnicity (Ἰουδαῖος). In other words, Ignatius isn't saying, "If a Jew speaks to you . . ."
Second, Ignatius' identification of the two hypothetical speakers in terms of "circumcision" [περιτομήν] and "uncircumcision" [ἀκρόβυστος] may simply be a result of Pauline influence (see Romans 2). But given my immediately preceding point as well as the emphasis on action rather than belief for the word Ἰουδαϊσμός, the "circumcision/uncircumcision" language likely continues the focus on behavior. Ignatius isn't telling the Philadelphians to avoid Judaism (as we understand the term, i.e. as a particular religious perspective) but rather those who espouse those set of practices that distinguish Jews from gentiles.
Third, Ignatius seems to be less critical of Jews who observe peculiarly Jewish practices than gentiles (= gentile Christians, I presume) who do so. For the circumcised Jew who proclaims Χριστιανισμόν ["Christianity"] is better [ἄμεινον] than the [circumcised?] gentile who proclaims Ἰουδαϊσμόν ["Judaism"]. In fact, the "uncircumcised man" [ἀκρόβυστος] who proclaims Judaism must have been circumcised if his proclamation of Judaism is to make any sense at all; the language of ἀκροβυστία must surely be metaphorical (even ironic) here.
Fourth, both speakers come under Ignatius' censure if they fail to speak of Jesus Christ. This raises the question, which Ignatius doesn't address, whether the bishop would have found acceptable a gentile proclaiming Judaic practices as long as he gave sufficient attention to proclaiming Jesus. In other words, was Ignatius' problem less about the idea of circumcision/Jewish distinctive culture and more with a phenomenological (or experiential) complaint that gentiles who found Jewish observances meaningful for their faith spent too much time expounding those observances rather than the message of/about Jesus?
Fifth [which, strictly speaking, is a question rather than an observation], how does the reference to "the names of men" (or "human [as opposed to "divine"?] names"; μόνον ὀνόματα ἀνθρώπων) relate to Ignatius' point? Is this simply an aspect of his metaphor of these speakers who neglect Jesus Christ as "tombstones and graves," or is this another way of speaking of his view of Ἰουδαϊσμός apart from the preaching of Jesus Christ? Is this, in other words, similar to the polemic in the Pastoral Epistles against [Jewish] genealogies (see 1 Tim 1.4; Tit 3.9)?