How do Christians reconcile Deuteronomy 13:1-4 with their belief in the abrogation of the Mosaic law? Deuteronomy 13:1-4 states:


All this word which I command you, that shall ye observe to do; thou shalt not add thereto, nor diminish from it.

If there arise in the midst of thee a prophet, or a dreamer of dreams--and he give thee a sign or a wonder,

and the sign or the wonder come to pass, whereof he spoke unto thee--saying: 'Let us go after other gods, which thou hast not known, and let us serve them';

thou shalt not hearken unto the words of that prophet, or unto that dreamer of dreams; for the LORD your God putteth you to proof, to know whether ye do love the LORD your God with all your heart and with all your soul.



My understanding is that Christians believe that Jesus abrogated the Mosaic law (e.g. keeping the Sabbath, dietary restrictions, etc.) and they no longer feel bound by them. How, then, do they understand the above passage, which states that one may not subtract commandments from the Law, and which seems to imply that a true prophet will not do so?
The historical answer for this, as it applies to Gentiles, was recorded on the book of Acts.  

Mosaic Law was given to the nation of Israel (the Jews), not the Church.  

Early on in Church history, the question of whether adherence to Mosaic Law was to be applied to Gentile believers.


  Acts 15
  
  New International Version (NIV) The Council at Jerusalem
  
  15 Certain people came down from Judea to Antioch and were teaching
  the believers: “Unless you are circumcised, according to the custom
  taught by Moses, you cannot be saved.” 2 This brought Paul and
  Barnabas into sharp dispute and debate with them. So Paul and Barnabas
  were appointed, along with some other believers, to go up to Jerusalem
  to see the apostles and elders about this question. 3 The church sent
  them on their way, and as they traveled through Phoenicia and Samaria,
  they told how the Gentiles had been converted. This news made all the
  believers very glad. 4 When they came to Jerusalem, they were welcomed
  by the church and the apostles and elders, to whom they reported
  everything God had done through them.
  
  5 Then some of the believers who belonged to the party of the
  Pharisees stood up and said, “The Gentiles must be circumcised and
  required to keep the law of Moses.”
  
  6 The apostles and elders met to consider this question. 7 After much
  discussion, Peter got up and addressed them: “Brothers, you know that
  some time ago God made a choice among you that the Gentiles might hear
  from my lips the message of the gospel and believe. 8 God, who knows
  the heart, showed that he accepted them by giving the Holy Spirit to
  them, just as he did to us. 9 He did not discriminate between us and
  them, for he purified their hearts by faith. 10 Now then, why do you
  try to test God by putting on the necks of Gentiles a yoke that
  neither we nor our ancestors have been able to bear? 11 No! We believe
  it is through the grace of our Lord Jesus that we are saved, just as
  they are.”
  
  12 The whole assembly became silent as they listened to Barnabas and
  Paul telling about the signs and wonders God had done among the
  Gentiles through them. 13 When they finished, James spoke up.
  “Brothers,” he said, “listen to me. 14 Simon[a] has described to us
  how God first intervened to choose a people for his name from the
  Gentiles. 15 The words of the prophets are in agreement with this, as
  it is written:
  
  16 “‘After this I will return
      and rebuild David’s fallen tent. Its ruins I will rebuild,
      and I will restore it, 17 that the rest of mankind may seek the Lord,
      even all the Gentiles who bear my name, says the Lord, who does these things’[b]— 18     things known from long ago.[c]
  
  19 “It is my judgment, therefore, that we should not make it difficult
  for the Gentiles who are turning to God. 20 Instead we should write to
  them, telling them to abstain from food polluted by idols, from sexual
  immorality, from the meat of strangled animals and from blood. 21 For
  the law of Moses has been preached in every city from the earliest
  times and is read in the synagogues on every Sabbath.”


More is available at Grace Communion International.


  Why, then, these four rules? Some scholars say the Jews believed that
  these laws dated back to the time of Noah, and therefore applied to
  all nations. Others say that all four rules were associated with
  idolatry. Some say that these four rules were laws of Moses, and were
  given so Gentiles and Jews could eat together. None of these
  suggestions is fully convincing. (See later for more details.)
  
  However, the decree makes it clear that Gentiles do not have to be
  circumcised, nor do they have to obey the laws of Moses. They are
  circumcised spiritually, not physically. God never gave those commands
  to the Gentiles.


...


  To summarize: Some men said that Gentiles should be circumcised and
  obey the laws of Moses or else they could not be saved. Not so, said
  the apostles. Gentiles are saved by grace and faith. God is pleased to
  dwell in people who aren’t circumcised and who don’t keep the rituals.
  But since Moses is widely preached, we need to give a decree that
  clearly distinguishes the Christian faith from the Law of Moses. This
  pleased the entire church, so they wrote it in a letter and sent it to
  Antioch, where they “were glad for its encouraging message”