Do Old Testament individual, family and social laws and guidance apply to Christians or did Jesus come to discard OT laws and guidance?

God gave us 10 commandments that no human can possibly fulfill for their entire life from birth to death without breaking at least one commandment at least one time (except Jesus). I believe the Sermon on the mount was to show US that we can't be perfect in the eyes of God. Most people can say with pride, "I never killed anyone" but how many can say "I never thought about it" or "I never hated anyone"? The point was to teach us "ALL have sinned and fall short of God's glory" so we wouldn't boast or throw stones with the attitude "yeah, I'm a sinner but I'm better than that guy" and yet that is exactly what we do and Christians are some of the worst. Some ministers even preach this without realizing the damage they are doing. There is no such thing as "acceptable sins". Taking a pen from work has less consequences than cheating on your wife but it is still stealing. We need to focus on loving the Lord and forgiving our brothers and the rest will come. Our actions reflect what is in our heart which is what God sees. We can't see another person's heart which is why we shouldn't judge others. We should worry about what God sees when he looks at us.

Because there can not be such thing as an objective proof, especially when the subject matter is as personal as one's connection to the divine, this answer can not be any more than a mere opinion. Therefore it seems safe to begin with "I think..."

I think the answer to your question lies in the phrase from the Old Testament, quoted by Jesus in the New Testament: "I desire love not sacrifice". What is a sacrifice in this context? It is a price to pay to purchase goods from God, that is a specified algorithm aimed at obtaining something from God. So it seems laws and sacrifice are the same thing in this respect, if their aim is your connection to Him. In other words if you are trying to purchase God's favor, or manipulate him through rules, payment, or incantations, you're not thinking your actions all the way through. From this perspective, one of salvation or connection, none of the laws ever applied to neither Christians nor the Jews.

So the reason those laws are presented in the scripture must be something other than salvation. In addition, interpreting those laws never was a straightforward affair. Moses, who delivered "thou shall not kill", led Israelites to kill the inhabitants of the Holy Land. Many Jews, living abroad, could not stone other Jews for adultery. How did they decide what scriptural laws were applicable, and when, was as much of a problem then, as it is now, and so one needs to know their purpose for them to have benefit.

It seems each law has to be considered individually, depending on the situation one's in. Can you afford to kill your own animals in a fantastic ritual? Maybe you should, it would certainly be more artistic and beautiful than mass machine slaughter at the meat factory, having no idea who touched your meat before you bought it at the supermarket. Should you stone people for adultery? If you live in a country that permits it, then you have God's permission to cleanse that country of it, of course accepting full well that you should present yourself and your family and children for stoning, for stonable offenses, should you or they commit such. Should you celebrate the prescribed holidays? Couldn't hurt, considering that people have no idea how to celebrate holidays these days, but as with all others your salvation does not depend on them.

The only things that were truly cancelled in the New Testament (by the apostles, not Jesus, nonetheless) was the circumcision, which wasn't quite a law, but more of a mark of an era, and the dietary restrictions, which seem very minor of the laws, and although I do not have an understanding of why they were given with the rest, I am inclined to believe that the point of them was prevention of some diseases that were common in those forbidden animals in the ancient times.

So nothing is changed, as long as your aims are not to manipulate God, following the rules of the Old Testament, as far as they are legal in your country, can improve your life, but discretion should be practiced and there are far more important things to be mostly concerned about, that the former should naturally flow from. Perhaps the phrase "law written on their hearts" pertains to that.

"The law which came 430 years later does not annual a covenant previously ratifed with Abraham." Gal 3:17. Abraham 'believed' God and it was counted as righteousness. Many years later he was circumcized in the flesh. He obeyed all God's laws, precepts and commandments. Law existed BEFORE the Mosaic Covenant. Salvation by faith = justified freedly. Works accompanying salvation if faith in action = santification. Jesus wants a chaste bride, not a lustful mare. 'Put to death whatever is of the flesh.' Crucify it. Your body is now a temple and must be presented as a holy sacrifice.

With regard to Jesus' "Do not think that I have come to abolish the Law and the prophets; I have not come to abolish but to fulfill," Gary Tuck presented an excellent paper where he made the case that the the 'not to X but to Y' language is a Hebraism understood as 'not only to X but also to Y.' One example Tuck gives is 1 John 3:18 where John doesn't mean that it is useless to vocalize love for someone; rather, the idea is to not only vocalize one's love but also show it in action. So the idea is "Do not think that I have come only to abolish the Law and the prophets; I have not come only to abolish but also to fulfill."

Paul seemed pretty clear that the Colossians were not to be judged according to food, drink, religious days, or Sabbaths (Col 2:16-17). He was also clear to the Romans any of the commandments is fulfilled by love to neighbor (Rom 13:8-10), implying that the Mosaic Law isn't binding upon Christians. The author of Hebrews is clear that the Mosaic Law is obsolete and passing away (Heb 8). These passages and others indicate that the Mosaic covenant is not binding upon Christians.

I don't know why you frame the question exclusively in terms of Jesus's direct teachings. The teaching of the Church begins with Jesus's teaching, it doesn't end there. Peter's dream, allowing non-kosher food, and conversion of Gentiles without circumcision, is as central to Christian doctrine as anything Jesus said, and from this dream it is 100% clear that the Mosaic law no longer applies to Christians converted from Gentiles. It is not clear whether Jewish converts were supposed to keep OT laws at first, but with time, the convention that OT laws are superseded by Christian teachings became established doctrine, and one does not discriminate between church members based on their ancestry.

Within Jesus's teaching, Romans and Samaritans can be righteous, more so than Jews who are overly concerned with nitpicking finer points of law. The rejection of law as a source of righteousness is also implicit in the calling to perfection, the idea that God's law goes far beyond some minor rules about hygene and sacrifice.

But Jesus does say "I come not to overthrow the law, but to fulfil it", but even if this is an injunction to keep the law, one shouldn't focus on minor contradictions and inconsistencies. I personally don't see it as contradictory, because of the context in which the statement is made. Jesus's is talking about a Jewish culture which is actively oppressed by Roman rule, where abandoning the Jewish law is considered a form of collaborationism. In this context, it is repugnant to abandon the Mosaic tradition, because you are abandoning those who are fighting oppressive colonialism against long odds.

But Peter's dream is in an entirely different context, the growth of Christianity through converts in the Roman empire itself. Within this context, it answers the question "What is required of people to become Christian?", and it gives a tolerant, forgiving answer, which does not nitpick fine points of Jewish theology, and does not require overly strict conditions on accepting Christ. This is consistent with the philosophy of Jesus teaching.

So from Peter's dream, the main answer is not to change their diet or cut their foreskin, but to get the message of Christ out. This is the most important thing.

The Church did not have the ambition of only liberating palestine from Roman rule, but of liberating the entire Roman empire from its cruel pagan traditions. How can one find fault with the practice that succeeded in doing this the fastest and most efficiently?

Further, the teachings of Christ require an open mind regarding best practice, and demand that goodness come from within, and not from outside. Imposing a strict law has the counterintuitive consequences at times of making bad actions seem ok, because they are not specifically contradicted by law. No Christian denomination spells out a strict all encompassing law, and leaves things open to change in response to new developments. This is considered a positive evolution within Christianity, and it seems that it is good.

"Do not think that I came to abolish the Law or the Prophets; I did not come to abolish but to fulfill. 18 For truly I say to you, until heaven and earth pass away, not the smallest letter or stroke shall pass from the Law until all is accomplished. 19 Whoever then annuls one of the least of these commandments, and teaches others to do the same, shall be called least in the kingdom of heaven; but whoever keeps and teaches them, he shall be called great in the kingdom of heaven." Matthew 5: 17-19.

It is clear from the above verses that Jesus did not come to discard the Law, even though a lot of churches do preach that. However, us as Gentiles are not required to follow the Law since the Law was mainly given to the Israelites and those who attached themselves to Israel (i.e. either were their slaves, servants or those who converted to Judaism).

When God sent Jonah to Nineveh, he asked that they repent and that was that, he did not demand that they follow the Law of Moses.

Jesus does ask us to follow his commandments. So whatever he said to us in the Gospels is what we should follow. Whether that means following the Law of Moses or not is a different matter (I, for one, don't believe that the Law is discarded or any such thing, God and his people have a lot of love for the Law of Moses. I don't believe God just sent it to tell people that they can't follow God's commands, I believe the Law is good and that we should use it as a guidance even if we don't follow it as legally and morally binding).

"He who has My commandments and keeps them is the one who loves Me" John 14:21

This is, of course, my opinion.

The short answer is that the OT law is not binding on Christians; instead we are called to something far greater, perfection.

The longer answer: this was actually the subject of the first recorded church summit. There they focused on the big issue of the day: circumcision. Was it a requirement for salvation? I will come back to the decision in a moment.

A number of fundamental strands of doctrine are woven throughout the NT, which I have elaborated on previously on this site. They include God's perfection, our sin and subsequent need of a Saviour. The law, therefore, was given to show us our sin, but it could not save us.

Jesus said on many occasions that the law was not enough. For example, He said that not only should we not murder, we should not even call someone a fool. He said not only should we not commit adultery, we should not even look with lust. He told us that we should not be rule followers but people of genuine righteousness. In summary, He called us to be perfect.

And, as James said and Paul echoed, if we break one part of the Law, we have broken all of it. So we start our Christian lives as law breakers.

So back to your question: does the Law apply to Christians? Should we try to keep the law? Absolutely not! If we try to keep the Law to please God or to earn our salvation then, as Paul said, Jesus will be of no value to us! Instead, inspired by God's love to us, our goal is to love God and love others. As James said, Paul said (twice) and as even Jesus Himself said, if we love God and love each other, we obey the whole Law.

Back to that church summit. The conclusion was advice to the Gentile believers avoid certain things, presumably so as not to be a stumbling block to others who might want to come to faith. It was certainly not a list of obligations required for salvation, nor has this short list featured substantially in church history. (If it was intended for salvation, it would not be complete, because it missed our fundamental "rules" like "don't murder"!)

So, why did Jesus say that "anyone who breaks one of the least of these commandments and teaches others to do the same will be called least in the kingdom of heaven"? From the references above, it seems clear that Jesus could not have been talking about the entire Law, including circumcision, or else much of the NT and church history would be wrong! It appears, therefore, that he was talking about His commandments, which He preached throughout His ministry but especially in the Sermon on the Mount.

Further suggested reading: The Sermon on the Mount (Matthew 5-7) and Paul's letter to a church struggling with this issue: Galatians.