Thayer's Lexicon defines NT use of the word [philosophy here as
a) used either of zeal for or skill in any art or science, any branch of knowledge. Used once in the NT of the theology, or rather theosophy, of certain Jewish Christian ascetics, which busied itself with refined and speculative enquiries into the nature and classes of angels, into the ritual of the Mosaic law and the regulations of Jewish tradition respecting practical life
It is clear that Apostle Paul was referring to his rivals headed by St. James in Jerusalem, who followed the Law. This happens more than once in his letters. He was referring to Jewish traditions [of men], not Greek.
However, as the first century drew to a close, some 50 years after Paul, Christians not only [by necessity] embraced Greek philosophy (Platonism), but early Christian apologetics, such as St. Justin Martyr, in his work First Apology, used the similarity of Christian briefs and teachings to that of Roman and Greek pagan beliefs and teachings as a justifiable raison d'etre for Christianity. Here is an example [my emphasis]:
Let's not forget the critical Hellenic influence on Christian thinking exerted by the first century Alexandrian Jewish scholar, Philo, mainly credited for introducing the idea of Plato's Logos (i.e. the Word) into Christian thinking. One can appreciate the scope of his influence by the fact the first Church historian, Eusebius of Cesarea (third century), refers to Philo as "St. Philo" (even though he is not reocngized as a Chirstian saint)!
Finally, if Paul's words to Colossian (2:8) were to be applied to Greek philosophy, and pagan religion, then John's Gospel becomes null and void. After all, it is St. John who, at the end of the first century, refines Philo's suggestions and Hellenizes Christianity (for reasons that correposnd to the reality of that time period) by identifying Jesus with Logos, in a complete break with the Jewish tradition of who the anointed one (i.e. the Jewish "meshiyah", or "christos" in Greek) is supposed to be.