You have put your finger on an issue that today is forbidden. This is to do something religious for purely practical purposes.Might I then ask you what was the purpose of having Paul agree to pay for the believers who were about to complete their oaths at the temple in Jerusalem, which Acts recounts. if the Christian community was so removed from Jewish customs? Paul even had shaved his head, according to Acts, which would be in compliance with some purely Jewish customs.
Note, I am not arguing that there was not movement away from Jewish customs, but Acts records continued observance even after Paul completed his third missionary journey, which fits with the time frame I posted of late 50's early 60's.
As for dating the Didache, that is problematic. It likely falls sometime after the early 70's, but that is about all that can clearly be stated, to be more precise is speculation.
In the Book of Acts, the leadership of the Jerusalem church advised the Apostle Paul to sponsor four Jewish believers who had taken a vow (likely a Nazarite vow). They instructed Paul to join them in the purification ritual and pay their expenses so the men could complete their vows. Paul agreed to this plan to prove to the Jewish community that he was still an observant, law-abiding Jew. By covering the costly sacrifices required by the Mosaic Law, Paul demonstrated solidarity with the Jewish believers in Jerusalem. Paul would never have been able to travel the Roman Empire preaching on Synagogues unless he was already a Jew in good standing.
The expenses covered Paul's own purification rites as well as the animal sacrifices required at the Temple to formally complete the men's vows. This event ultimately led to a riot in the Temple and Paul's arrest by Roman authorities. ....the path of good intentions.