This doesn't seem to square with NT Christianity. It seems to point more to the legalism of the OT where people were not saved and reluctantly kept the law under threat of death. They received material wealth for obedience and loss for disobedience.
In the New Covenant, only born-again believers exist in any true sense. Granted, among false professors. And we dig to identify sin to get rid of it. There is nothing more repulsive to the born-again heart than the sins that would rob us of our Spiritual fruit.
I think that there are two issues here.
You are absolutely correct that in the New Covenant only born-again believers exist in any true sense. Even as we try to root out sin from our behavior (and the behavior of our church) there will always be tares among the wheat. We are faced with this as a fact (do not pull the tares because we may be pulling wheat kinda thing). I think that some will be shocked to hear the words "I never knew you". That is a sad and terrifying thing.
The other issue is sin in our own lives. People tend to like to point out the sins of others without examining themselves. They look for the splinter in the eye of the brother while ignoring the log in their own eye.
I gave an example where a man made false accusations against me. I think he probably just made a mistake and misunderstood, but that does not matter. I focused on his accusations and insulted him. What I should have done (and did later) was look at the "log" in my own eye, address my own sin before pointing to the sin in this man. That was pride in my own heart that expressed itself in self-justification. I did not want to be wronged and I wanted people to know exactly why that man's accusations were false. What I should have done was simply comment that he had made a mistake and ignored any continued false accusations.
My own actions ended up as an act to cover up my sin (my sin of unforgivness, of pride, of insulting the man) by pointing to his sin of making false accusations about me.
Some times our attempt to "root out" sin in other people are just that - an attempt not to deal with the sins in our own lives.
If someone makes enough noise perhaps others will not see their sin. But the problem is that the more noise they make the more obvious their sin becomes.
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