To whomever the author is referring with the word “Hypocrites” (as translated in the text), they are clearly not welcome. A possible clue as to why lies in the treatment of the Lord's Day assembly: “...No one quarreling with his brother may join your meeting until they are reconciled.” This statement, taken with another, more broad observation concerning the end-times mythology found later on the reading: “when lawlessness is on the rise, men will hate and persecute and betray one another,” may indicate one of the core thought processes of these early followers.
It is reasonable to assume that “lawlessness,” was an ancient concept, even in the time of Tiberius. All religions and theologies are essentially systems of order and control if they involve themselves in morality and organization. One of the many challenges early people faced was the threat to themselves by those other humans they encountered. Such concerns are evident in early Christian tradition. Like Temple, Church is intended as a public place, and Christianity as a public organization that isn't easy to get into and doesn't look fondly on outsiders who might disrupt progress and disturb peace. The specific nature of the instructions given in the Didache imply the function of ritual in maintaining this integrity. Each prayer would take even modern students some time to learn, and this would require practice. This practice would require commitment, which could be demonstrated in other ways when found.
Through these instructions, a framework was put in place that might naturally produce leadership, visible in deed and adherence, to the groups that were commanded to “elect bishops...to render the sacred services.” Perhaps the early Christians had an antagonistic relationship with the Jews, though “A Cloud of Witnesses” relates that the two groups might have otherwise been indistinguishable,” but as translated, the Didache seems unconcerned with this relationship. Certainly the Pharisees and Sadducees would not have looked favorably on the new movement who insisted on prayer to a man who lived and died. But though the Didache doesn't reflect much more than disdain for the unconverted in general, the tone and message of these instructions does seem to regard conflict and quarreling as unproductive and undesirable.