Ok, Christ’s sacrifice actually, finally accomplishes righteousness in man by not only remitting sin but by giving us the grace, the power of the Spirit, to overcome it now. By placing our faith in Him this grace becomes effective-working- in our lives. But no mere law-keeping, including keeping the ten commandments, means or guarantees righteousness or sinlessness in us. So regardless of who wrote Hebrews, Paul explains the difference in Phil 3:9:
“…not having a righteousness of my own that comes from the law, but that which is through faith in Christ—the righteousness that comes from God on the basis of faith.”
Once it’s understood that this is a real righteousness that is given as a result of faith in Christ then we begin to see the difference between the old and new covenants more clearly IMO-and this is how the churches in the past have historically taught it.
I believe you are miss understanding the word of God, and Paul writing. First let me say that God had Peter to clearly warn us about some of Paul’s writing. (2Peter:3:15-16) (v.15) And account that the longsuffering of our Lord is salvation; even as our beloved brother Paul also according to the wisdom given unto him hath written unto you; (v.16)
As also in all his epistles, speaking in them of these things; in which are some things hard to be understood, which they that are unlearned and unstable wrest, as they do also the other scriptures, unto their own destruction. Now let us take heed to this warning, we can’t ignore all the bible and just concentrate on a hand full of verses out of the writings of Paul. Because some of Paul’s writing is hard to be understood.
The verses you are quoting are true but they are not referring to us having a sinless life, because Paul says in (Rom. 4:15)
Because the law worketh wrath: for where no law is, there is no transgression. If there is no law there is no sin. What Paul is saying in Phil 3: 7 But what things were gain to me, those I counted loss for Christ. 8 Yea doubtless, and I count all things but loss for the excellency of the knowledge of Christ Jesus my Lord:
for whom I have suffered the loss of all things, and do count them but dung, that I may win Christ, 9 and be found in him,
not having mine own righteousness,
which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith: 10 that I may know him, and the power of his resurrection, and the fellowship of his sufferings, being made conformable unto his death;
See when you keeping the Laws (Commandment) of God you lose that you may gain life in Christ. Its always the righteousness of God and not yours because you won't know what righteousness was, if God didn't tell you. Now Paul said in (Rom. 3:23-25) (v.23)
For all have sinned, and come short of the glory of God. (v.24)
Being justified freely by his grace through the redemption that is in Christ Jesus: (v.25)
Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God. So the bible tells you to
repent and be baptized in the name of Jesus for the remission of sins, and ye shall receive the gift of the Holy Ghost." (Acts 2 :36-38). And by doing so you come up under his precious blood and then you
are saved from your sins that are past, not present or future sins but for sins that are past.
“But now apart from the law the righteousness of God has been made known, to which the Law and the Prophets testify. This righteousness is given through faith in Jesus Christ to all who believe.” Rom 3:21-22
“For if, by the trespass of the one man, death reigned through that one man, how much more will those who receive God’s abundant provision of grace and of the gift of righteousness reign in life through the one man, Jesus Christ!” Rom 5:17
“You have been set free from sin and have become slaves to righteousness.” Rom 6:18
And then Paul can tell us in Rom 7 that even the ten commandments, listing several, right as they are, cannot effect the righteousness in us that they point to-they serve only to convict us of unrighteousness, of sin, in fact. Rom 8 continues on:
“For what the law was powerless to do because it was weakened by the flesh, God did by sending his own Son in the likeness of sinful flesh to be a sin offering. And so he condemned sin in the flesh, in order that the righteous requirement of the law might be fully met in us, who do not live according to the flesh but according to the Spirit.”
“Therefore, brothers and sisters, we have an obligation—but it is not to the flesh, to live according to it. For if you live according to the flesh, you will die; but if by the Spirit you put to death the misdeeds of the body, you will live. For those who are led by the Spirit of God are the children of God.” Rom 8:3-4, 12-14
Only God can make man righteous. We must turn to Him in faith-and remain in Him. If we turn back to the flesh, to persistent, grave sin, we’re not in Him, we’re no longer His children until and unless we have a change of heart-and turn back.
Paul objected to the idea that works of the law could make one just or righteous, and that applied to the whole law, while being "under the law". Being under grace, however, means that we can finally accomplish the obedience that the law calls for but could not accomplish. It all hinges on our being in a state of communion with God, which itself is the very basis and essence of justice/righteousness for man. It's what we were made for, and it's entered into by faith. .
When the bible speaks of laws we no longer have to keep, it is speaking of the sacrificial laws. These laws were a school master pointing us to the fact that Jesus would be sacrificed for our sins. Since Jesus died we are no longer under a school master, (required to offer up bulls and goats for our sins).
Now we must believe (have faith) Jesus died for us (Hebrews 10:4,9-10) 4
For it is not possible that the
blood of bulls and of goats should take away sins. 9
then said he, Lo, I come to do
thy will, O God. He taketh away the first, that he may
establish the second. 10
By the which will we are
sanctified through the offering of the
body of Jesus Christ once for all.
This doesn't mean we don't have to obey God's moral laws of conduct. That would be like a man getting paroled from prison and then ignoring the same laws that sent him to prison in the first place. Jesus only died once, so if we willingly break God's law, after accepting Jesus, our reward will be eternal damnation (Hebrews 10:26-27) 26
For if we sin wilfully after that we have received the knowledge of the truth, there remaineth no more sacrifice for sins, 27
but a certain fearful looking for of judgment and fiery indignation, which shall devour the adversaries. Let us avoid this at all costs, seeking a better reward. Jesus will return real soon
And, behold, I come quickly; and my reward is with me, to give every man according as his work shall be. (Revelation 22:12).