Sometimes, humanly speaking, we know when a person is not a Christian. If they say they are not a Christian, or if they don’t know a thing about Jesus, or if their life (words and deeds) has absolutely no fruit, most likely the person is not a Christian. However, we should not go around making statements on who is and who is not a true Christian. It’s not biblical, healthy, or productive to constantly make declarations on who is and who is not a believer. (As a side, it might be a mark of hyper-calvinism to frequently make declarations on a the spiritual state of people.)
In Reformed theology – following Scripture – there’s a great term: “judgment of charity” (or “charitable judgment”). This means that if a person professes the Christian faith, shows some fruit in his or her life, and is involved in a Christian church, we treat the person like a Christian and refuse to constantly doubt his faith. It’s a covenantal concept. Calvin talked about this in Institutes IV.i.8; Owen, Ridgley, Boston, Bavinck, Berkhof and other Reformed theologians also used these terms. In Scripture, Paul called the straying Galatians brothers and the impure Corinthian church saints (for just two examples).
J. C. Ryle notes how the judgment of charity is a Christ-like attitude which is comforting, and which we should emulate:
Let us take comfort in the thought that the Lord Jesus does not throw off his believing people because of failures and imperfections. He knows what they are. He takes them, as the husband takes the wife, with all their blemishes and defects, and, once joined to him by faith, will never put them away. He is a merciful and compassionate High Priest. It is his glory to pass over the transgressions of his people and to cover their many sins. He knew what they were before conversion—wicked, guilty and defiled; yet he loved them. He knows what they will be after conversion—weak, erring and frail; yet he loves them. He has undertaken to save them, notwithstanding all their shortcomings, and what he has undertaken he will perform.
Let us learn to pass a charitable judgment on the conduct of those who claim to believe. Let us not set them down in a low place and say they have no grace, because we see in them much weakness and corruption. Let us remember that our Master in heaven bears with their infirmities, and let us try to bear with them too. The church of Christ is little better than a great hospital. We ourselves are all, more or less, weak, and all daily need the skillful treatment of the heavenly Physician. There will be no complete cures till the resurrection day.