New Covenant = New Law
Under the New Covenant there are no outward day keeping commandments (days,month,seasons or years - Galatians 4:10). We may give special days to the Lord such as Christmas but these are not commanded as something that we must do. (Romans 14:5,6) Sadly there are some "christians" that are saying that we must obey Jewish commandments and ceremonies - just as they were fighting for this in apostle Paul's day. Let us accept the sufficiency of Jesus Christ and be careful regarding these issues. Do not be afraid to point these things out to fellow believers. - Brother Eric
A covenant means an arrangement made between two people through which they enter into a certain relationship. It is not, in the biblical usage, an ordinary agreement, because the contracting parties enter into an ordinary agreement on equal terms. But in the biblical sense of covenant, it is God who is the prime mover and approaches man to offer him a relationship upon conditions which man could neither initiate nor alter but only accept or reject.
The word Paul uses for new when he speaks of the new covenant is the same as Jesus used and it is very significant. In Greek there are two words for new. First, there is neos (Greek #3501), which means new in point of time and that alone. A young person is neos (Greek #3501) because he is a newcomer into the world. Second, there is kainos (Greek #2537), which means not only new in point of time, but also new in quality. If something is kainos (Greek #2537) it has brought a fresh clement into the situation. It is the word kainos (Greek #2537) that both Jesus and Paul use of the new covenant, and the significance is that the new covenant is not only new in point of time; it is quite different in kind from the old covenant. It produces between man and God a relationship of a totally different kind.
Some people even today follow strict outward rules which "have an appearance of holiness and spiritual maturity" but we are not to confuse such issues with true Christian worship and practice. Some encourage all to keep certain dietary laws. Such practices can make one feel more "justified". All asceticism issues are basically dealing with some kind of self-justification. As Christians Jesus Christ has justified us and made us holy unto Himself. - Brother Eric
Followers of Christ are told to deny self (Luke 9:23), but asceticism takes this command to an extreme. The Bible never suggests that a Christian should purposely seek out discomfort or pain. On the contrary, God has richly blessed us “with everything for our enjoyment” (1 Timothy 6:17). The Bible warns of those who “forbid people to marry and order them to abstain from certain foods” (1 Timothy 4:3); thus, it is erroneous to believe that celibates who abstain from certain foods are “more holy” than other people. We are under grace, not under the law (Romans 6:14); therefore, the Christian does not live by a set of rules but by the leading of the Holy Spirit. Christ has set us free (John 8:36). In many cases, the ascetic practices self-denial in order to earn God’s favor or somehow purge himself from sin. This shows a misunderstanding of grace; no amount of austerity can earn salvation or merit God’s love (Ephesians 2:8-9). (From here)
Scripture for those who wish rules
(such as vegetarianism & day keeping)