The argument is approaching its grand finale. The Mosaic Law is finished as a covenantal means of relating to God. Heb 10:1 could not be clearer: the Law was a shadow of all the good things Jesus brought. When the reality to which the shadows pointed arrived then shadows were obliterated in the sunshine of his brilliance and glory.
This shadow comprised of Old Covenant religion, here referring to sacrifices (10:1) and, more broadly, "religious duties" (10:11).
What did these things do for the Old Testament worshipper? They didn't cleanse them internally, in their consciences, from sin. While they provided outward purification, they didn't remove the stain of (correctly) feeling guilty (10:2). IN fact they did the opposite - the acted as a constant, year-in, year-out reminder of sin and guilt that never went away (10:3). Imagine all the paraphenalia of your religion telling you all the time "you are guilty before God" but never doing anything about it. Always accusing but never relieving guilt. Horror!
Worse still, the people had forgotten that this was all the Law and the sacrifices was meant to do, and had instead convinced themselves that they were the way to please God and come to him. God was never pleased with the sacrifices, that wasn't what they were for (v6 & 8). So put yourself in their place: you earnestly believe that offering them again and again is the thing that God wants to please him. But it doesn't matter how many times you do it, it doesn't work and you can't figure out why. You are stuck in an endless whirl of religious duty that never satisfies and never achieves what you think it ought to achieve.
The answer of course is the final, perfect, efficacious sacrifice of Jesus that did achieve what the animal sacrifices didn't. The Ps40 quote in v5 has two parts to it: God was not pleased with the sacrifice of animal burnt and sin offerings (v5-6), but he was pleased with the final offering of Jesus' life (v7).
So, the writer concludes, the first is set aside in order to establish the second (v9). We can now please God because of Jesus. However, this is mutually exclusive with trying to please him by religious duty. That is set aside in order to have Jesus. You can try one or the other but not both (and one will fail you).
The summary is one of my all time favourite verses (10:14): by one sacrifice he has made perfect for ever those who are being made holy
Just let that wash over you for a minute. If you are in Jesus was are declared by God to be perfect for ever because of Jesus. How can that be true? Because his perfect righteousness is credited to your account. Because God declares that you will now never be blamed for your sin. You have been cleansed. You will no longer be held guilty. You are eternally redeemed. Your sins and lawless acts are not remembered by God, they are forgiven (v17).
And, critically, where they are forgiven there is no longer any need for ongoing sacrifice for sin (v18).
Therefore I conclude that if you are trusting your performance of religion to please God - whether apparently Christian or not - you will utterly fail. That was the mistake in the Old Testament, trusting their dutiful religion. Not only didn't it work, but it was never the point anyway. Religion will obscure the real answer for you and take you away from it. The real answer is that if you trust Jesus Christ you ARE accepted, you ARE forgiven, you ARE welcomed by God, eternally and unshakeably. If you don;'t fee it, then it is your feelings that are faulty. They need to come into line with the reality that God declares about you.
Any Christian out there who is trusting your own holiness, your own church attendance, your own good works, your own morality or your own Christian ministry thinking that you get brownie points with God for them, I urge you to stop, repent of it right now, and turn to him with utter thankfulness for the righteousness of Jesus given to you absolutely freely and for nothing.