According to the scriptures, a true Christian is a person who believes (fully trusts) in Jesus Christ as their Savior for forgiveness of sins and eternal life; one who belongs to Christ and has been born again to new life in Christ.
Are Christians perfect; no and will not be so until entering the eternal state. Christians are each at different places in their life in Christ. That’s why the Bible speaks about maturity and immaturity because it is a process. Nevertheless, a true Christian should be growing in the fruits of the Spirit...
...love, joy, peace, longsuffering, kindness, goodness, faithfulness, gentleness, self-control. Against such there is no law (Galatians 5:22-23),
while continuing to turn away from the works of the flesh...
...adultery, fornication, uncleanness, lewdness, idolatry, sorcery, hatred, contentions, jealousies, outbursts of wrath, selfish ambitions, dissensions, heresies, envy, murders, drunkenness, revelries, and the like... (Galatians 5:19-21)
If you see someone who claims to be a Christian, yet shows no real interest in submitting their life to Christ or who continues to constantly live out the works of the flesh listed above without any repentance...then it’s reasonable to question their relationship to Jesus. On the other hand, a real Christian may mess up sometimes, act selfish, commit some minor or even major sin, but listens to the Holy Spirit’s conviction, is very repentant and change is demonstrated over the course of their life. Ultimately, I think it’s best to leave the judgement of who is a real Christian to God. Yet, God calls believers to use wisdom and discernment; a so-called Christian pastor who comes across as righteous and good in public, but abuses his wife and children in private is a deceiver and I think it can legitimately be said... he is NOT a Christian. Just one example.
So how is it that atheists, Muslims, etc. may live what appear to be lives morally superior to a lot of Christians? My answer is that everyone is made in the image of God. Therefore, everyone has an awareness of God’s morality instilled within them and are capable of doing some good and altruistic things. Probably even a Nazi who killed or abused Jewish men, women and children went home and treated his family and dog kindly. But that doesn’t erase his vicious, cruel behavior committed against the Jews or God. What is done against God’s creation is also done against Him. No matter how moral one may think they are, the reality according to the scriptures is that everyone falls short and sins against others and God and all are in need of the Perfect Savior.