Are we, as Christians, bound by Old Testament law? Conservative Christians sure like to think we are. This is largely because they enjoy the whole "sinners in the hands of an angry god" meme as it frightens them into abstaining from doing "naughty" things. But most Christians say that we aren't completely bound by them anymore and I am one of them. Of course, the Bible says two different things so it's up to each one of us to take the time to study the material and context of what is being said. This article breaks it down quite nicely.
Many traditional Christians have the view that only parts are applicable, many Protestants have the view that none is applicable, dual-covenant theologians have the view that only Noahide Laws apply to Gentiles, and a minority have the view that all are still applicable to believers in Jesus and the New Covenant.
The entire link identifies and describes the various views and has sublinks with well sourced material on the study of the meaning of the passages listed above. Take some time to read through all of it. It becomes clear rather quickly that the people who believe that all of the OT is still applicable are very much in the minority.
I fall into the category of only parts of the Old Covenant are applicable although it's interesting to note that there are many who believe none are. So, the Abrahamic Covenant, the Land Covenant, and the Davidic Covenant are out. An eye for an eye is now gone, as Christ directs in Matthew 5. All of the ceremonial laws are no longer applicable either.
But what about sin? The Old Testament clearly states that God punishes sinners. But with the New Covenant of Jesus, that is longer true. Take note of the verses used in this link. Look familiar?:)
Indeed, the father of Protestantism understood this very well. Martin Luther explained this as Justification by Faith. He wrote “Faith alone is the saving and efficacious use of the word of God.” He then looked to Romans Chapter 10, verse 9 as being absolutely fundamental for believers in Christianity. The passage states, “If you confess with your lips that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved.” This was his justification of faith. One did not need to pay a penance for sins, whether through confession or indulgences, to get into heaven (recall that indulgences, or the paying of money or service to the church, was one of his major gripes with Catholicism). One simply needed to believe that Christ was God and that he was resurrected and then they would be saved. Luther explained justification this way in his Smalcald Articles:
The first and chief article is this: Jesus Christ, our God and Lord, died for our sins and was raised again for our justification (Romans 3:24-25). He alone is the Lamb of God who takes away the sins of the world (John 1:29), and God has laid on Him the iniquity of us all (Isaiah 53:6). All have sinned and are justified freely, without their own works and merits, by His grace, through the redemption that is in Christ Jesus, in His blood (Romans 3:23-25). This is necessary to believe. This cannot be otherwise acquired or grasped by any work, law, or merit. Therefore, it is clear and certain that this faith alone justifies us...Nothing of this article can be yielded or surrendered, even though heaven and earth and everything else falls (Mark 13:31).
I bolded the parts that Christian conservatives seem to have trouble understanding in terms of sin, faith and confession. In framing the argument regarding indulgences in this way, Luther was able to remove the people that had inserted themselves between the common man and the Lord: the papacy. Interestingly, Christian conservatives have assumed the role of Pope these days, saying that they and only they are interpreting the Bible correctly. Luther had something to say about them as well.
…Every baptized Christian is a priest already, not by appointment or ordination from the Pope or any other man, but because Christ Himself has begotten him as a priest…in baptism.
What this means is that every man who is baptized and accepts Christ is no less a valid interpreter of the Bible than anyone else. All that is needed are the Five Solas. This launched a larger critique on the leadership of the Roman Catholic Church. In On Papal Power, Luther wrote “when the attempt is made to reprove them with the Scriptures, they raise the objection that only the pope may interpret the scriptures” In the early 16th century, the pope had the final say on exactly what was meant by the scriptures, not Luther and certainly not the common man. Luther saw this, along with the authority to issue decrees and convening councils as theft, writing, “they have cunningly stolen our three rods from us, that they may go unpunished”
Further, Luther abhorred the decadence of the church, stating that they were hiding behind self created authority “so that they can practice all the knavery and wickedness which we see today” Luther’s teachings were a direct threat to Rome. If people simply looked to the Bible and got their faith “free” from God, with no intermediaries, how long would it take for the power of the papacy to erode? The flow of financial rewards to the church would ebb as well. Luther also challenged church authorities by asserting that there was no hierarchy leading up to God. All men were priests and equal in the eyes of God.
Thus, members of the clergy should not have special accommodations or privileges. Luther again...
Every baptized Christian is a priest already, not by appointment or ordination from the Pope or any other man, but because Christ Himself has begotten him as a priest…in baptism. (But) the preaching office is no more than a public service which happens to be conferred on someone by the entire congregation all the members of which are priests.
The office of the priest is one that is democratically elected by all of the people, not by papal order. He is no more closer to God than anyone else. This is how Luther’s argument became a much broader threat to church leaders and led to deep erosion with them as well as the clergy. He laid the foundation for Protestantism which, at its core, rejects intermediaries or interpreters of what the Bible "really means."
If, at this point, Luther sounds very New Testament heavy, it's because he is. Recall the New Covenant.
The Christian view of the New Covenant is a new relationship between God and humans mediated by Jesus which necessarily includes all people,both Jews and Gentiles, upon sincere declaration that one believes in Jesus Christ as Lord and God. The New Covenant also breaks the generational curse of the original sin on all children of Adam if they believe in Jesus Christ, after people are judged for their own sins, which is expected to happen with the second arrival of Jesus Christ. Thus as the Apostle Paul advises that the Mosaic Covenant of Sinai does not in itself prevent Jews from sinning and dying and is not given to Gentiles at all (only the Noahic covenant is unique in applying to all humanity), Christians believe the New Covenant ends the original sin and death for everyone who becomes a Christian and cannot simply be a renewal of the Mosaic Covenant since it seemingly accomplishes new things.
New things indeed. This would be where the grace part comes into play. There was no grace in the OT but now there is with the sacrifice of Jesus.
So, we aren't really bound by parts of the Old Testament any longer. There are no sinners in the hands of an angry god. Since this is the case, it puts into question many OT ideas (see: homosexuality, noun, not mentioned in the Ten Commandments or by Jesus at all) and, thus, it follows logically that some of it is just wrong. As a people, we evolved culturally over the time period between the OT and the NT and grew spiritually.
Recall that Jesus said, "If thou wilt enter into life, keep the commandments. He saith unto him, Which? Jesus said, Thou shalt do no murder, Thou shalt not commit adultery, Thou shalt not steal, Thou shalt not bear false witness, Honour thy father and thy mother: and, Thou shalt love thy neighbour as thyself." This last one is His New Commandment, detailed in John 13: 33-35.
Little children, yet a little while I am with you. Ye shall seek me: and as I said unto the Jews, Whither I go, ye cannot come; so now I say to you. A new commandment I give unto you, That ye love one another; as I have loved you, that ye also love one another. By this shall all men know that ye are my disciples, if ye have love one to another.
Seems pretty straight forward to me.