On the other hand, Matthew 5:17ff does not originate with Mark. Its correspondence in Luke 16:16f suggests that it is at least partly from the "Q" source, which is older than Mark and suggests a "fully Jewish Jesus".
Btw, quite a number of scholars have suggested that the sentence "whoever breaks one of the least of these commandments, and teaches others to do the same, will be called least in the kingdom of heaven" is a hostile allusion to Paul and his "law-free Gospel" (which in turn influenced Mark)...
Yes, the non-Markan material in Matthew (e.g. the Matthean redaction of Q and M) is thought by Koester and others to originate in a Syrian Jewish-Christian community that saw itself as opposed to both Paul and Pharisaic Judaism. Here is something I wrote the other week on this matter:
Paul was viewed as "lawless" and a "worker of lawlessness" because he rejected the Law (i.e. he was literally Law-less), whereas Jewish-Christian groups such as the Ebionites and Nazoreans believed that Jesus was the True Prophet who came to reinterpret the Law and replace the false Pharisee halaka with the true understanding of the Law. They also did not believe that the death and resurrection of Jesus was itself the mode of salvation (cf. the concept of Jesus as a substitionary sacrifice for sin); rather, they believed that Jesus was the only person to fully live according to the Law and was thus saved from death, and anyone who lives according to the way of Jesus would also likely be saved by their "works," by how they lived -- just as Jesus was saved himself from death. The epistle of James (which, incidentally, was not really written by James, but as most scholars believe was a product of the Jewish-Christian community), the Didache, the Ascents of James, and the Kerygma Petrou present a similar view. In fact, James appears to be a point-counterpoint to Paul's epistle to the Galatians. They present contradictory views on the Law which are not totally irreconcileable but clearly opposed to each other to some extent:
"We had to become believers in Christ Jesus no less than you had, and now we hold that faith in Christ Jesus rather than fidelity to the Law is what justifies us, and that no one can be justified by keeping the Law....In other words, through the Law I am dead to the Law, so that now I can live for God...I cannot bring myself to give up God's gift: if the Law can justify us, there is no point in the death of Christ....Take Abraham for example: he put his faith in God and thus faith was considered as justifying him. Don't you see that it is those who rely on faith who are the sons of Abraham? Scripture foresaw that God was going to use faith to justify the pagans....On the other hand, those who rely on the keeping of the Law are under a curse, since scripture says: 'Cursed by everyone who does not persevere in observing everything prescribed in the book of the Law. The Law will not justify anyone in the sight of God....the Law is not even based on faith....If you do look to the Law to make you justified, then you have separated yourselves from Christ, and have fallen from grace....Tell those who are disturbing you [i.e. teaching conformity to the Law] I would like to see the knife slip [i.e. castrate themselves]....The Law has now come to an end with Christ and everyone who has faith may be justifed. If your lips confess that Jesus is Lord and if you believe in your heart that God raised him from the dead, then you will be saved" (Galatians 2:16-21; 3:5-12; 5:4, 12; Romans 10:4, 9).
"The man who looks steadily at the perfect Law of freedom and makes that his habit -- not listening and then forgetting, but actively putting it into practice -- will be happy in all that he does. Nobody must imagine that he is religious while he still goes on deceiving himself and not keeping control over his tongue; anyone who does this has the wrong idea of religion. Pure, unspoilt religion, in the eyes of God our Father is this: coming to the help of orphans and widows when they need it...The right thing to do is to keep the supreme Law in the scriptures : "You must love your neighbor as yourself," but as soon as you make distinctions between classes of people, you are committing sin, and under condemnation for breaking the Law. You see, if a man keeps the whole of the Law, except for one small point at which he fails, he is still guilty of breaking it all . It was the same person who said, 'You must not commit adultery' and 'You must not kill'. Now if you murder, you do not have to commit adultery as well to become a breaker of the Law....Take the case, my brothers, of someone who has never done a single good act but claims that he has faith. Will that faith save him ? If one of the brothers or one of the sisters is in need of clothes and has not enough food to live on, and one of you says to them, 'I wish you well; keep yourself warm and eat plenty,' without giving them these bare necessities of life, then what good is that? Faith is like that: if good works do not go with it, it is quite dead....Do you realize, senseless man, that faith without good deads is useless. You surely know that Abraham our father was justified by his deed, because he offered his son Isaac on the altar? There you see it: faith and deeds were working together; his faith became perfect by what he did....Anyone who slanders a brother, or condemns him, is speaking against the Law and condemning the Law. But if you condemn the Law, you have stopped keeping it and become a judge over it. There is only one Lawgiver [i.e. Jesus] and he alone is the only judge and has the power to acquit or to sentence. Who are you to give a verdict on your neighbor" (James 1:25; 2:8-24; 4:11-12).
The anti-Pauline rhetoric can also be detected in the Matthean redaction of the Sermon on the Mount, which also takes James' point of view on the Law and the worth of good deeds versus faith in salvation:
"Let your light shine before men in such a way that they may see your good works, and glorify your Father who is in heaven. Do not imagine that I have come to abolish the Law or the Prophets. I have come not to abolish but to complete them. I tell you solumnly, till heaven and earth disappear, not one dot, not one little stroke shall disappear from the Law until its purpose is achieved. Therefore, the man who infringes even one of the least of these commandments and teaches others to do the same [e.g. Paul] will be considered the least in the kingdom of heaven; but the man who keeps them and teaches them will be considered great in the kingdom of heaven....You must therefore be perfect [i.e. perfect in following the Law] just as your heavenly Father is perfect. Be careful not to parade your good deeds before men to attract their notice; by doing this you will lose all reward from your Father in heaven...Do not judge and you will not be judged, because the judgments you give are the judgments you will get, and the amount you measure out is the amount you will be given....So always treat others as you would like them to treat you; that is the meaning of the Law and the Prophets...A sound tree cannot bear bad fruit, nor a rotten tree bear good fruit. Any tree that does not produce good fruit is cut down and thrown on the fire. I repeat, you will be able to tell them by their fruits. It is not those who say to me, 'Lord, Lord,' [e.g. confessing Jesus as Lord] who will enter the kingdom of heaven, but the person who does the will [i.e. by works, by following the Law] of my Father in heaven. When the day comes many will say to me, 'Lord, Lord, did we not prophesy in your name, cast out demons in your name, work many miracles in your name?' Then I shall tell them to their faces: I have never known you, away from me, you who practice lawlessness (literally, anomian "without Law")....Truly I say to you, whatever you shall bind on earth shall be bound in heaven; and whatever you loose on earth shall be loosed in heaven" (Matthew 5:15-19; 6:1; 7:1, 18-23; 18:18).
Again, contrary to what Paul wrote, the Law did not "come to an end with Christ," and salvation comes not from confessing Jesus as "Lord, Lord" but from "good works" as taught in the Law. Like James , the Matthean redactor emphasizes that one should not "judge". This applies to both judging others, as well as taking it upon oneself to judge the Law as invalid. Paul does both throughout Galatians -- such as declaring the Law "dead" and wishing his opponents to castrate themselves. And note that Paul is the one who "teaches others" to set the Law aside, and such a person is described "the least in the kingdom of heaven". And the references to "binding" and "loosing" in Matthew 18:18 refer specifically to a halakic interpretation of the Law that Jesus confers to his apostles (which Paul, the "apostle to the Gentiles," rejects). So it is clear that the Pauline view is not the only one in the NT; there is a dynamic response to Paulinism which continued in other Jewish-Christian works such as the Kerygmata Petrou, the Epistola Petri, and the Ascents of James. For example, the Epistola Petri condemns "the lawless and absurd doctrine of the man who is my enemy," a clear reference to Paul, and goes on affirm his commitment to the Law of Moses in a response to Paul's claims in Galatians 2:11-14:
"Indeed, some have attempted, while I [Peter] was still alive, to distort my words by interpretations of many sorts, as if I taught the dissolution of the Law and, although I was of this opinion, I did not express it openly. But that may God forbid! For to do such a thing means to act contrary to the Law of God which was made known by Moses and was confirmed by our Lord in its everlasting continuance" (Epistula Petri 2:3-5).
There was also an incredible diversity of views on what Jesus represents and his origin. Some believed that Jesus was only a prophet, others believed that he was a man filled with divine Wisdom from heaven, while others believed that he was divine Wisdom that had come down from heaven. Others believed that "Jesus" was merely the fleshly recepticle of the heavenly being, and some thought that his flesh was only an illusion and he was entirely divine. Some thought that Wisdom, or the Holy Spirit, descended on him before birth, while others believe it came upon him during his baptism. Some thought that he became anointed as the Christ during his baptism or during his resurrection. Some thought he was a "righteous angel," others thought he was nothing less than God himself. All of this was part of fabric of early Christianity, and it is hard to trace the priority of some over others. This is partly because the Judaism that Christianity developed out of was also far from homogenous (e.g. the Essenes, Pharisees, Saducees, etc.) and thus some Jews drew heavily on Hellenistic concepts of the Logos and Sophia, while others fit Jesus more into the OT prophet template, and others drew on a more political concept of the Messiah. Some drew more on proto-gnostic dualist concepts and others did not. It is clear that Paul himself drew largely on proto-gnosticism and had a very different concept of Jesus than is presented in the historicizing synoptic gospels. The gospel of John is more in the gnostic vein, but itself (in its later redaction) parts company with gnosticism by insisting that the "Word" was creator. It was very complex, far more than could ever be accurately reconstructed after the fact. That Christians had completely different ideas about who Jesus was can be seen in the confessional statements of Matthew 16:13-16 and Thomas 13:1-4.