The Didache is not long. Perhaps it would be helpful to go through the whole text and point out differences you see. That might be more productive than looking at second-hand characterizations of the text.
For instance,
I don't think it is likely that the text is saying to avoid "Jewish Christians." In fact, the reference to the preparation day in the same sentence referenced does not suggest the sort of disapproval we have of Jewish Christians keeping the law as we see in Justin Martyr, or more forcefully in Chrysostom at a later time.
The description of the "hypocrites" and the relating of the Lord's prayer suggest the ones they are not to imitate are the pharisees:
Didache. The Teaching of the Twelve Apostles (translation Roberts-Donaldson). On Early Christian Writings.
www.earlychristianwritings.com
But let not your fasts be with the hypocrites, for they fast on the second and fifth day of the week. Rather, fast on the fourth day and the Preparation . Do not pray like the hypocrites, but rather as the Lord commanded in His Gospel, like this:
Our Father who art in heaven, hallowed be Thy name. Thy kingdom come. Thy will be done on earth, as it is in heaven. Give us today our daily bread, and forgive us our debt as we also forgive our debtors. And bring us not into temptation, but deliver us from the evil one; for Thine is the power and the glory for ever.
Pray this three times each day
Luke 18 shows the Pharisee in Jesus' parable fasting twice a week:
Luke 18:11 The Pharisee stood and prayed thus with himself, God, I thank You that I am not like other men—extortioners, unjust, adulterers, or even as this tax collector. 12 I fast twice a week; I give tithes of all that I possess.’ (NKJV)
The context of the Lord's prayer included reference to the hypocrites, which did not seem to be related to "Jewish Christians":
Matthew 6:5 “And when you pray, you shall not be like the hypocrites. For they love to pray standing in the synagogues and on the corners of the streets, that they may be seen by men. Assuredly, I say to you, they have their reward. 6 But you, when you pray, go into your room, and when you have shut your door, pray to your Father who is in the secret place; and your Father who sees in secret will reward you openly. 7 And when you pray, do not use vain repetitions as the heathen do. For they think that they will be heard for their many words.
8 “Therefore do not be like them. For your Father knows the things you have need of before you ask Him. 9 In this manner, therefore, pray:
Our Father in heaven,
Hallowed be Your name.
10 Your kingdom come.
Your will be done
On earth as it is in heaven.
11 Give us this day our daily bread.
12 And forgive us our debts,
As we forgive our debtors.
13 And do not lead us into temptation,
But deliver us from the evil one.
For Yours is the kingdom and the power and the glory forever. Amen. (NKJV)
See also:
Matthew 23:13-14 13 “But woe to you, scribes and Pharisees, hypocrites! For you shut up the kingdom of heaven against men; for you neither go in yourselves, nor do you allow those who are entering to go in. 14 Woe to you, scribes and Pharisees, hypocrites! For you devour widows’ houses, and for a pretense make long prayers. Therefore you will receive greater condemnation. (NKJV)
I think there is still a discussion to be had on
- Fasting on two different days than the pharisees
- Praying the Lord's prayer three times a day
in regards to the biblical statements. But by going through the actual text and comparing it to the text of Scripture you would at least be eliminating the middle-man of the scholar's statements, drawn from a curated source.