A Christian is justified—saved from sin, death, and hell—by grace alone, through faith alone, in Christ alone.
What makes a Christian "Christian"? The Gospel and the gifts do, full stop. The Holy Spirit "calls us by the Gospel, enlightens us with His gifts, sanctifies and keeps us with Christ in the true faith," wrote Martin Luther in his Catechism. For Lutherans, since the Reformation, this short explanation of the Third Article of the Creed expresses powerfully and elegantly what makes a Christian a Christian. But isn't there more? Isn't there something of our doing that has to be done if we're to be sure we're amongst those who refer to themselves as "Christian"? What do you mean, just the Gospel? You mean some ordinary, earthly words, water, bread and wine makes a person God's own child? Yes. That's it. Full stop. Just the Gospel and God's gracious, faith-inducing, life-renewing, eternally comforting gifts.
A Christian is justified—saved from sin, death, and hell—by grace alone, through faith alone, in Christ alone. All this happens through the preaching of the Gospel of Christ Jesus and the deliverance of His gifts. In Christ, God holds nothing of Himself back from us. There's nothing untrue about the Gospel or the gifts. Nothing confusing, conditional, or held in reserve by God until He decides we're worthy or deserving.
That means that when anything is added to the definition of what makes a Christian a Christian, other than Christ's all-sufficient life, death, and resurrection for us, we push back. Why? Because anything that's not Christ for us isn't Gospel. Not the true Gospel anyway, not the way God would have it delivered to us gratis, for Christ's sake, as free gift.
But what about works commanded by the Law? Surely the purpose of God's Law is salvation. If a person doesn't take seriously God's commands in the Law, he's not really a Christian, right? Faith without works is dead, after all.
That's not true. As Martin Luther wrote in his commentary on Galatians 2:4-13, this kind of theologizing is wrong: "The true Gospel declares that good works are the embellishment of faith, but that faith itself is the gift and work of God in our hearts. Faith is able to justify, because it apprehends Christ, the Redeemer."
Where we get confused and go wrong is that outside of Christ Jesus we can only think in terms of the Law. It makes sense to us—ultimate, logical, a matter of life or death sense to us—that what earns us God's favor, causes God to pay attention to us, and ultimately reward us, is what we've done and left undone.
But, in Christ, the Christian looks only to Jesus, the Son of God, who gave Himself up to death for the sin of the world. Only when he turns his eyes away from Jesus crucified does a man fixate on God's Law and wander away from Christ, away from grace. Then, no matter what he does or doesn't do, he is no more a Christian than a Muslim or Jew is a Christian.
What makes a Christian "Christian" is the Gospel of Jesus Christ. Faith clings to Jesus dead and risen for us, leans on Him, and has eyes only for Him. Outside of Christ there is only blindness and guess-work about what makes a Christian a Christian. Then works, and obedience, and earning rewards, and avoiding God's punishment become the defining characteristics of a Christian. Then he has no idea what a Christian is because he doesn't look to Christ crucified. He doesn't know what faith is, and can't teach it to other people.
But through the Gospel and His gifts, Christ calls us to true faith. Faith that looks only to Him for everything we need for body and soul, here and hereafter. Jesus is the Author and Perfector of our faith. He is our Wisdom and Righteousness, our Redemption and Sanctification. In Christ through faith we don't have to ask what makes a Christian "Christian" any more than a bride wonders about her beloved when she stands, hands intertwined with his, facing her bridegroom before the altar as he speaks his vows.
Christ makes a Christian "Christian." He alone, and nothing else. No conditions. No qualifications. No limits or measures imposed upon us by our Heavenly Father. Just Christ and Him alone. Our Lord and our God. Our Savior, who will never leave or forsake us because He has put His Name on us when He baptized us, and He cannot forsake Himself.
What makes a Christian "Christian" is a matter of the Gospel, and nothing else.