From the POV that all will have their works tried through fire, it's not sin as a barrier between God and man that is a problem. In the old testament, sin put a barrier between God and man. (Strangely, still today almost all of Christendom claims that there is still a barrier of sin between God and man. They don't see the sacrifice!!)
But through Jesus Christ, God has put away sin.
So you're question about sinning is somewhat errant. Sin is not the problem. The "problem" is that what we sow is what we shall have when we stand before God. If we sow unrighteousness in this life (ie. killing our neighbor), the flames of purification will be hotter.
In fact, judgment may be more "severe" than if there were still yearly sacrifices. This is because the perfect sacrifice has been provided, and yet man spites this Gift.
In reality, Christendom doesn't understand the Gift, and it teaches that we still need to be forgiven, when we are all actually already covered.
Paul, in his letters/epistles, gives a lot of commandments. Do this, do that, don't do this..... Seems like the law? Well, it would, except that the restitution has been made. God is now calling all men (and women :) ) to walk in righteousness.
Still, many spite this calling, or don't understand that they are under the Blood. And that's no little thing!
I'm writing this, but still trying to understand what I myself am writing. Or maybe I don't fully understand it.
The only thing I'm thinking about is, what is making a sacrifice all about? (For we know that grace is UNMERITED favor.)
Love to all,