What is the basis of not following Halakha?

The Laws of the Old Testament can be put into three categories as mentioned: Civil, Ceremonial, and Moral.

Civil Law

I dont know about you, but I am an American citizen. I live under the American Civil law, and glorify God by obeying the "law of the land." The Civil laws of the Old Jewish state really have no bearing on me, a gentile outside of that country.

Ceremonial Law

Ceremonial Law, Sacrafices, worship etc. Well first off, most of these apply to the Levitical priesthood, which I am not a jew, and have to access nor right to. But most importantly, Hebrews tells us that

HEBREWS 10:11-22 11 And every priest stands ministering daily and offering repeatedly the same sacrifices, which can never take away sins. 12 But this Man, after He had offered one sacrifice for sins forever, sat down at the right hand of God, 13 from that time waiting till His enemies are made His footstool. 14 For by one offering He has perfected forever those who are being sanctified. 15 But the Holy Spirit also witnesses to us; for after He had said before, 16 “This is the covenant that I will make with them after those days, says the Lord: I will put My laws into their hearts, and in their minds I will write them,”[c] 17 then He adds, “Their sins and their lawless deeds I will remember no more.”[d] 18 Now where there is remission of these, there is no longer an offering for sin. Hold Fast Your Confession 19 Therefore, brethren, having boldness to enter the Holiest by the blood of Jesus, 20 by a new and living way which He consecrated for us, through the veil, that is, His flesh, 21 and having a High Priest over the house of God, 22 let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience and our bodies washed with pure water.

Please read the book of Hebrews, it is really great in tying the Old and New together.

So, Christ is the High Priests, he has Achieved the righteousness of the Law for us (Which we could never ever do). As told in the books of Acts, Peter reasons about gentile disciples being taught to following the Laws of Moses.

Acts 15:6b-12 Peter rose up and said to them: “Men and brethren, you know that a good while ago God chose among us, that by my mouth the Gentiles should hear the word of the gospel and believe. 8 So God, who knows the heart, acknowledged them by giving them the Holy Spirit, just as He did to us, 9 and made no distinction between us and them, purifying their hearts by faith. 10 Now therefore, why do you test God by putting a yoke on the neck of the disciples which neither our fathers nor we were able to bear? 11 But we believe that through the grace of the Lord Jesus Christ[a] we shall be saved in the same manner as they.”

See how he calls the law a "yoke which we neither we nor our fathers could bear"

Paul tells us in Romans 3:20

For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin.

Keeping that law can NOT save anyone, but breaking the law is Sin and condemns the whole word before God.

So Paul Clarifies for us. Romans 4:3

What does Scripture say? "Abraham believed God, and it was credited to him as righteousness."

So even from as far back as Abraham, being made right with God has come through Faith!

Ephesians 2:8-9

For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; 9not as a result of works, so that no one may boast.

Putting faith in our works and our ability to "keep the law" is actually a dangerous snare called "legalism." It is a snare because what we are doing is putting out faith in OUR OWN WORKS as opposed to in the FINISHED WORK of CHRIST.

God's MORAL LAW.

Gods moral law is traditionally spelled out in the 10 commandments, but is often found in other places of scripture also. These let us know about Gods Character, and his requirements for human conduct.

The bible says in 1 Pet 1:16

since it is written, “You shall be holy, for I am holy.”

God requires purity on the inward parts

psalm 51:6 Behold, You desire truth in the inward parts,

Gods Moral law shows us Gods character, and helps us to see ourselves in truth. (as sinners who have violated the law). The Fact is that Telling Lies is Wrong! Stealing is Wrong! Coveting is Wrong! Adultery is Wrong! Murder is Wrong! and such are the commandments.

They are holy and good, but they can't save you, because we have all already sinned and broken Gods law. Some people comfort themselves saying "Well I havent ever murdered anyone, im not really that guilty."

But the bible says in James 2:10

For whoever keeps the whole law and yet stumbles at just one point is guilty of breaking all of it.

The law stands and accuses us, we can't use it to clean ourselves up! We need someone to pay the penalty for us, God demands Justice!

This is what Jesus did on the Cross.

Most Christians do not believe that they are changing or ignoring any law. However, there are many laws which certain Gentile Christians do not believe apply directly to them.

In the early days of the church, as chronicled in the book of Acts, there was some division on how Gentiles should respond to the various laws held by the Jews, such as the Kosher food laws. Paul and Peter initially disagreed, and there was a council held to consider the question. The decision was that Gentile converts would not have to become Jews and follow their laws, but instead were only bound by certain laws, which were very similar to those given to Noah. This is in the book of Acts in chapter 15. Outside of the Bible, this is often called the Council of Jerusalem.

Most Christian denominations would consider any law that is outside of the Torah itself to be extra-biblical, and therefore, only of interest to gain context on the law that is written in the Torah. When Jesus spoke, he pointed out several occasions where the current Jewish law of his day contradicted the actual Law of the Torah, or at the very least, was practiced in a way that was opposed to the original purpose. The reason that Jesus had to say that he was not breaking the law, as you quoted, was because many people believed he was doing just that when he challenged the traditions of the day. For instance, he picked corn and healed on the Sabbath, and he didn't necessarily keep the custom of washing before eating. In those cases, he would explain how the current practice was not actually part of the law given by God and cite the Scriptures in support.

With regards to the the laws directly in the Torah, some Christian denominations will divide those into categories of ceremonial, civil, and moral law. The ceremonial laws, like performing sacrifices, have already been fulfilled in Christ, and as such, doing so again would be equivalent to putting Christ on the cross again. Also, there is currently no proper temple for the performing of the sacrifices, and so these are impossible to properly fulfill. Civil law would be those portions of the law which were designed to create a framework for society within Israel. Many of these were never intended to apply to people outside of country Israel, and some only applied to Jews inside of Israel. Most of these laws would not work well without the framework that God setup for that state, and so could not be properly practiced elsewhere.

This would leave the moral laws, and there are a variety of opinions between denominations on how to approach these. One way some approach them is to say that the majority of the Levitical Law was given "because of the hardness of their hearts." In other words, they weren't actually intended for Gentiles, but to express the character of God and emphasize holiness and principles that the Jews could not understand otherwise, and function as pictures for the rest of us. Those groups tend to lean on Paul's teachings that salvation is by faith alone, and that the law does not save, but only shows that we need salvation. Other denominations claim that the 10 commandments are what were meant to apply to all people and follow them alone. There are some denominations which do try to follow all the laws.

Another point that is important to understand is that many Christians believe that passages like Isaiah 52:15, and many verses like the ones listed here: Are there Old Testament Scriptures that mention salvation for the Gentiles?, imply that God's intention was always to provide a method of salvation to the Gentiles, and that even though we are grafted into Israel, by Christ, we do not have to individually become Jews to experience salvation. Previously, those who desired salvation would convert, and then become bound by the law, where this is not the case after the promise was fulfilled.

I am not currently aware of any Christian denomination which would think they are actually changing laws. Generally, their goal is to do away with man-made laws, and then to understand God's Law as well as they can with the new understanding that the law has been completely fulfilled in Christ, and that because of the sins of Israel, God's grace has now been poured out on Gentiles also. The various disputes arise over how best one should correlate those truths.