The Hallmark of Judaism Judaism can never change its doctrines through the ages. Judaism had only been fulfilled.

Both the Jewish Bible (Old Testament) and the New Testament agree to the unchangeable laws in the Jewish Bible. It is easier for our universe to disappear than anything in the Jewish Bible to change, says Jesus. Even the establishment of the 'faith or belief of Jesus' movement does not affect the Law and the Prophets in the slightest way.

The Hallmark of Judaism: Judaism can never change its doctrines through the ages.

(17) You should not infer that I came to demolish the law or the prophets. I came not to demolish, but to fulfill. (18) For verily, I am saying to you, Till heaven and earth should be passing by, one iota or one serif may by no means be passing by from the law till all should be occurring. Matthew 5:17-18 CLV

Yet it is easier for heaven and earth to pass by than for one serif of the law to fall. Luke 16:17 CLV

You will observe to do just as Yahweh your Elohim had enjoined on you. You shall not withdraw to the right or to the left. Deuteronomy 5:32 CLV

`Only, be strong and very courageous, to observe to do according to all the law which Moses My servant commanded you; you do not turn aside from it right or left, so that you do act wisely in every [place] whither you go;" Joshua 1:7 CLV

Every word which I am enjoining on you today, you shall observe to obey it. You shall neither add to it, nor shall you subtract from it. Deuteronomy 12:32 CLV

Christian Judaism is pure Judaism of Moses and the Prophets, without the sacrificial system which was fulfilled (Matthew 5:17-18), because Jesus says that Salvation is from the Jews (John 4:22) and upholds Judaism in Luke 16:27-31. Yet, the Apostles distinguish and contrast the Judaism of the rebellious portion of the Jews with the Christian or Messianic Judaism in which the Messiah substitutes 'the works of the Law' to give rise to a brand of Judaism taught as the 'faith or belief of Jesus (Galatians 2:16). 

We may no longer keep the holidays of Moses and their associated sabbaths and animal sacrifices because Jesus fulfilled them, in addition to the fact that the rites in Moses were to be performed ONLY in Jerusalem, at the Temple, and by the priesthood. The seventh day sabbath lives on because because it is the signature memorial of the Creation works by Jesus and it preceded the sabbaths in Moses. Jesus commands the remembrance of His death as our Passover Lamb. Do we hold the remembrance only at the annual Passover date or any time we feel like it?

Also. neither Jesus nor the Apostles created a movement named Christianity. Jesus refers to all (Jews and Gentiles) who believe in Him as His followers. The Gentiles named the followers of Jesus Christians, just as the followers of any other good or bad charismatic leader are named after their leaders. So, there is no such separation as Judaism and Christianity. There has been and there will only be Judaism for the salvation of men (John 5:39). Jesus is the Author of Judaism and lived as a Jew under the Law of Moses, whom He emphasizes as the sure guide to His salvation.

Again, Jesus says that salvation is from the Jews not from the Christians. Christianity does not save. Judaism does, according to Jesus in John 5:39. Christian Judaism is founded in Moses and the Prophets. And Christianity? The followers of Jesus follow Jesus and His culture of 'belief or faith of Jesus' (Galatians 2:16, Acts 24:24). Christians of Christianity follow a blend of paganism and Judaism with more emphasis in paganism. Those blenders are not Jesus-Christians of the 'belief of Jesus) and, remember, the blending phenomenon is nothing new (Acts 20:28-32). The Apostles already witnessed apostasy from the Gospel of the 'faith of Jesus forming roots and the antichrist Christian movement and its false teachings. That is why they admonish us to be vigilant. For example, the Epistle to the Hebrews addresses, among other doctrinal issues, the false teaching that Jesus was an Angel (Hebrews 1). So does Jude (Jude 1:9).

The Gospel of repentance and remission of sins of the 'belief of Jesus' introduced by John the Baptist is not for the Jews only (John 3:16). It was just to be witnessed FIRST to them.

From the Apostolic teachings vantage point, the faith of Jesus or the belief of Jesus is neither Judaism nor Christianity: Jews must drop the works of the law and their sabbaths to believe in Jesus and Christianity must drop all its unscrupulous and flagrant affronts of the immutable Judaism of the belief of Jesus (Galatians 2:16, John 3:16, Matthew 5:17, Luke 16:17).

John came, who baptized in the wilderness and preached the baptism of repentance unto remission of sins.  Mark 1:4 ASV

And he came into all the region round about the Jordan, preaching the baptism of repentance unto remission of sins;  Luke 3:3 ASV

and that repentance and remission of sins should be preached in his name unto all the nations, beginning from Jerusalem.  Luke 24:47 ASV

Him did God exalt with his right hand to be a Prince and a Saviour, to give repentance to Israel, and remission of sins.  Acts 5:31 ASV

Christian Judaism aka the 'belief (faith) of Jesus'