This has more to do with how we interact with others and examination.
I have noticed a trend among conservative Christians that teach evidence of salvation. I have noticed a "spiritual gift" of fruit inspector arise. I have even heard of churches refusing people because they don't see a person have enough faith or fruit. I have seen people criticized, condemned, and disheartened to the point of leaving Christian fellowship. Then I have seen these same people justify it as these people were not really saved. This saddens, but doesn't surprise me. Satan will cause extremes to try and make the work of Spirit ineffective. I think that is why the Bible mentions so often how we should love each other. It is love that stands out and speaks volumes to unbelievers. Yet, on the other side, we are not to "love" to the point we throw out doctrine. The Bible IS doctrine and God finds it important enough to have written a whole book about it. It is a delicate balance. I picture truth and love on opposite sides of board balancing on a point of a rock with a chasm on each side. Leaning too much either way is dangerous.
We must teach examination of fruit. Why? Because the Bible commands it. We must show mercy, love, grace, support, and help bearing each other weaknesses. Why? Because the Bible commands it. Again it is a balance thing. Everything we do must be done in love. If we approach another confessing believer with sin, our motivation must always be love. We see a path a person is traveling or a stronghold in someone's life and can see the destruction it is or will bring. We approach that person because we are concerned. It hurts us to see this in their life and the fruit of it. We can see it affects their relationship with God and others. If they are unrepentant, yes the Bible lays out a plan of action.
This is different from imperfections and working out of faith. This is different from the natural struggle and growth of one's faith. This is different from being weak. A Christian who is growing is humble and willing to be taught. It doesn't mean they will agree with everything being taught... there is room for interpretation and application to different lives to "grey" areas. However, they will have a desire to know God's heart and follow it. 1 John says we will love His commandments and desire to walk in the light.
We do not know what goes on in the heart. I do not think the Bible really says we are to judge one's salvation. We are to judge their works. James tells us that faith without works is dead and useless. Therefore if we don't see works/change in a life what does it tell us. There isn't evidence of salvation. The sinful man in 1 Corinthians was the repentant man in 2 Corinthians. In the first, they were told to "treat" him as an unbeliever or actually worse than an unbeliever. The standard is higher for those who claim to be Christian and the consequences harsher. We are not to judge those of the world. Was the man in 1 Corinthians "saved"? ... yes. It is evidenced by his repentance in 2 Corinthians. They were then told to embrace him. You see, they didn't judge his salvation.... they judged his actions. It brought the man back to God. Evidence of a true believer.
Now most professing Christians don't have such blatant sins in their lives. What are we to do with them? If they are not mature, they won't be leaders. If they live immature Christian lives, love them and teach them. If they live worldly lives, I would treat them as unbelievers. How do I treat unbelievers? Well love them and carefully choose my involvement in their life and their influence in mine. Pray and pray and continually pray for everyone. Does my consideration of their salvation change the truth of it in their lives? No.
Examination needs to be taught. It could be a matter of heaven or hell. It especially needs to be taught that a person needs to examine his self. That is what is the most beneficial. Be careful teaching that saying a prayer saves you or telling someone that you think they are saved. We need not to judge but constantly point to scripture. Only self-examination can really work that out in someone's life. Let God confirm or convict ... do not interfere in the work of God.