I hadn't heard of Phocylides, either the man or the Sentences ascribed to him, until Roger Pearse brought the latter a few days ago. It happens that this Pseudo- work, after a surge of interest in the Reformation, got back into scholarly attention in 2017.
The consensus up to then was about where the Jewish Encyclopaedia left it: the book used Jewish law and Jewish literature, up to Ben Sira and the "Wisdom of Solomon". In turn, the second Sibylline up to v. 148 parallels vv. 5-79; which means their parallel about abortion must also be that Sibylline's paraphrase, directly, from our Sentences. But that is about it for Judaism (and the second Sibyl is usually deemed Christian anyway), unless you count Josephus. Jonathan Klawans in 2017 proposed "The Pseudo‐Jewishness of Pseudo‐Phocylides":
On definitional grounds, it is problematic to speak of a Jewish work that displays no distinctive Jewish concerns.
On evidentiary grounds, we know that the work was transmitted and used by Christians, and we can establish that its selective approach to biblical ethics aligns with identifiably Christian priorities. A Jewish provenance can be hypothesized, but we need not imagine a Christian context for the work.
Finally, on moral grounds, we must avoid prejudicial assumptions, such that only a Jew could know the Pentateuch well enough to produce The Sentences.
Pseudo-Phocylides's Jewishness is a pseudo-Jewishness. The evidence suggests its Christian use, its Christian allegiance and, therefore, its Christian authorship.
Michael Cover, er, covers this in "Jewish Wisdom in the Contest of Hellenistic Philosophy and Culture" ed. The Wiley Blackwell Companion to Wisdom Literature (2020), 229-47; doi 10.1002/9781119158288.ch13. He doesn't believe Klawans. There's also John Poirier, The Invention of the Inspired Text, 58-66 although I haven't read this. I have to say, I'm not believing Klawans either.
I understand that arguing for Jewish morality among the gentiles remains a popular genre to this day, as witness Dennis Prager's commentaries upon Genesis and Exodus. So there goes the first "problematic". That the Sentences enjoyed
Christian use is, I am sorry, a terrible argument. Philo and Josephus were abandoned by Jews and transmitted by Christians, but nobody calls those two Christians. Likewise the books of Maccabees and Ben Sira persisted among the Christians, and so did Enoch and Jubilees, and Tobit. As for the evidence of alignment with Christian priorities, see also Prager; and, we're seeing these same priorities in Philo and Josephus. Klawans should not read the twelfth-century ghetto into first-century Jewry.