In The Year of Living Biblically: One Man's Humble Quest to Follow the Bible as Literally as Possible, did the author, A. J. Jacobs, succeed in following the whole Bible literally? Was he following the whole Bible when he examined his clothing for mixed fibers?
To believe the Old Testament Law literally is to believe that this was the covenant God made with the ancient nation of Israel--a set of instructions for running their nation. To believe the New Testament literally along with the Old is to believe that when we were joined to Christ, we died with Him and were raised with Him, causing us to be released from the Law. From Romans 6-7:
Do you not know that all of us who have been baptized into Christ Jesus have been baptized into His death? Therefore we have been buried with Him through baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life. . . .
Do you not know, brethren (for I am speaking to those who know the law), that the law has jurisdiction over a person as long as he lives? For the married woman is bound by law to her husband while he is living; but if her husband dies, she is released from the law concerning the husband. . . . Therefore, my brethren, you also were made to die to the Law through the body of Christ, so that you might be joined to another, to Him who was raised from the dead, in order that we might bear fruit for God. . . . Now we have been released from the Law, having died to that by which we were bound, so that we serve in newness of the Spirit.
The purpose of the Law is to show us that we can't be perfect, even if we know exactly what we're supposed to do. In fact, having the Law only makes people want to rebelliously break it more (just like any child will want to do what you tell him not to do). In other words, "through the commandment sin would become utterly sinful" because the commandment reveals and provokes our innate rebelliousness against God.
The purpose of revealing these things through the Old Testament Law is to drive us to trust in Christ for forgiveness and life. Paul explains in Galatians 3:
Before faith came, we were kept in custody under the law, being shut up to the faith which was later to be revealed. Therefore the Law has become our tutor to lead us to Christ, so that we may be justified by faith. But now that faith has come, we are no longer under a tutor. For you are all sons of God through faith in Christ Jesus. For all of you who were baptized into Christ have clothed yourselves with Christ.
This is why a literal interpretation of the Bible tells us we are not bound to follow all the stipulations of the Old Testament Law.
The Law came in so that the transgression would increase; but where sin increased, grace abounded all the more, so that, as sin reigned in death, even so grace would reign through righteousness to eternal life through Jesus Christ our Lord. (Romans 5:20-21)