Clearly, Jesus was a Hebrew, the crowning glory of the Hebrews, but following him does not require adopting his culture.
The Hebrew Roots Movement is a grass roots movement by many Christians who are awaking to the simple fact that modern "Churchanity" is not found in the Christian holy book, the Bible. Wikipedia has an article about the Hebrew Roots Movement listing its seven features and variations of them. We will cover them point by point in this series warning about Hebrew Roots Movement and its pitfalls.
The first point is quoted below.
Both the Old and New Testaments are held as holy books, but the Old testament takes precedent over the New. The Torah serves as the foundation to all subsequent understanding and interpretation of Scripture. A foundational distinction of the Hebrew Roots movement is the manner in which Scripture is translated and interpreted so that later testimony (particularly the New Testament, or "Brit Chadashah") does not conflict with Torah commandments. It is believed by those in the Hebrew Roots movement that Yeshua the Messiah did not come to establish a new religion or to “do away” with the law. http://en.wikipedia.org/wiki/Hebrew_Roots
While this statement might seem reasonable at first glance, it has problems which perhaps only well Bible versed Christians might notice. It is true that Jesus taught the Torah and the prophets only, not anything new as is supposed by many Christians. Nonetheless, Jesus' atoning work was a new thing in the annals of Hebrew thought. It was not that it was actually new nor hidden but that Israel had not considered the heart of the Mosaic Law, just the letter. The letter of the Law was squeezed, manipulated and twisted by the Pharisees. Jesus said he was "untwisting" it and presenting it truthfully.
This untwisting is not obvious in English translations, not because it is hidden but because it is in plain sight but obscured by modern ignorance of Jesus' culture. The key to understanding what he did is in a Rabbinical Idiom, in the use of the phrases "Abolish the Law" vs "Fulfill the Law". Modern Christians think "Fulfilling the Law" annuals it, making it of non-effect in modern times. That is the opposite of the idiom. These two phrases relate to how the Mosaic Law is taught. If it is taught rightly and accurately, the teacher is said to be "Fulfilling the Law". If he misinterprets Moses, he is said to be "Abolishing the Law" or destroying it. The obvious conclusion of an accurate understanding of the text is Jesus "Fulfilled the Law" by teaching Moses and the Prophets accurately and truthfully.
But that is only a part of the story. The whole point of Jesus' teaching ministry was to open the eyes of Israel to the reality that their promised Messiah was present with them. This is embodied in the statement "The Kingdom of Heaven (God) is Near". Of course the Kingdom was near, its King and Jehovah's representative on earth were present right now, in their midst! But he had a mission to accomplish. His atoning work, of death and resurrection accomplished the final teaching of the Mosaic Law: The atonement for sin.
There is no point to atonement if there is no resulting benefit. This is the point the Hebrew Roots Movement misses. The benefit is a freeing from the letter of the Law, subject to man's interpretation, to a realm of the spirit of the Law which is not subject to man's interpretation. By graduating into the spirit of the Law, man is freed from the tyranny of other men's interpretations and forced adherence to a doctrinal point of view. Jeremiah said it best when he prophesied of this change:
 Behold, the days are coming, declares the LORD, when I will make a new covenant with the house of Israel and the house of Judah,
 not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt, my covenant that they broke, though I was their husband, declares the LORD.
 But this is the covenant that I will make with the house of Israel after those days, declares the LORD: I will put my law within them, and I will write it on their hearts. And I will be their God, and they shall be my people.
 And no longer shall each one teach his neighbor and each his brother, saying, Know the LORD, for they shall all know me, from the least of them to the greatest, declares the LORD. For I will forgive their iniquity, and I will remember their sin no more.
This is the benefit of Jesus' atoning work, the covenant relationship with Israel was built into man via holy spirit. This was complete on the day of Pentecost in the first century when the spirit Jesus had was offered freely to all of mankind, to the Jew first and then to all non-Jews (gentiles). Missing that is to miss Jesus' atoning work altogether. Emphasizing Torah keeping is nothing less that Judaizing Jesus' followers. This was the point of contention between the apostle Paul and the "zealous for the Law" Jews in Jerusalem. This point was settled by the first council in Jerusalem, recorded in Acts 15. The Hebrew Roots Movement ignores the apostles' decision in this first crisis in the new Christian movement. Essentially the decision was to avoid really angering the Jews but otherwise, let the gentiles live as they pleased, abiding by the loving dictates of their spirit from Jesus.
There are many passages which validate this decision and explain it.
But a Jew is one inwardly, and circumcision is a matter of the heart, by the Spirit, not by the letter. His praise is not from man but from God.
II Corinthians 3:4-6
 Such is the confidence that we have through Christ toward God.
 Not that we are sufficient in ourselves to claim anything as coming from us, but our sufficiency is from God,
 who has made us competent [sufficient] to be ministers of a new covenant, not of the letter but of the Spirit. For the letter kills, but the Spirit gives life.
Putting the faithful under the Mosaic Law and its interpreters is the opposite of the first church council's decision and the opposite of what the apostle Paul taught. People require this practice and submit to it for man's praise. You either have confidence toward God or you need the praise of man to feel good about yourself. Which will it be for you?
II Thessalonians 2:15
So then, brothers, stand firm and hold to the traditions that you were taught by us, either by our spoken word or by our letter.
We are to stand strong, unmovable in the teachings of Paul to the church. But the Hebrew Roots Movement countermands Paul's instructions and subjects the church to their interpretations and the letter of the Law. They would put a burden upon Jesus' followers, require diet restrictions and observance of Jewish holidays.
Therefore let no one pass judgment on you in questions of food and drink, or with regard to a festival or a new moon or a Sabbath.
Scripture could not be more clear. Paul taught the Hebrew concept of the deity. Paul taught the Hebrew world view. Paul taught the Hebrew belief system. But he did not teach keeping the lifestyle of the Jews in Torah Observance! The Hebrew Roots Movement attempts a noble thing to reform Christianity to its roots but fails miserably to free believers from the bondage of sin conscienceness which was the whole point of Jesus' atoning work. The Hebrew Roots Movement is correct in theory but fails in practice. It keeps men in fear of sin instead of the freedom in Christ to represent Jehovah in our world, just like Jesus did in his world. The Hebrew Roots movement is a far cry from the reality of Christ In You, the Hope of Glory.
To them God chose to make known how great among the Gentiles are the riches of the glory of this mystery, which is Christ in you, the hope of glory.