If a person believes Jesus is God are they now saved ?
I'm not entirely comfortable conflating being saved with being a Christian. These aren't necessarily synonymous, but more of an overlapping Venn diagram.
I'd look to Ephesians 2:8-10 as helpful here. Verses 8-9 tell us what saves us (and what does
not save us); that is, God saves us entirely out of His grace for us, through faith which is His gift and work; it is not our works which do this. Verse 10 tells us what we are saved for, we were saved for good works. Being a Christian isn't in merely that we have been, and are being, saved; being a Christian is in following Jesus.
The Christian life is found in two ways: Faith and works. Through faith alone we receive what God freely gives out of His grace; so that the Christian lives in Christ by faith (Justification); by our works we live out our life in God toward the world, toward our neighbors, in love, we walk in a new obedience borne of God's grace by the power of the Holy Spirit in lives of charity--love--toward others, thus the Christian lives in his/her neighbor by love.
It is impossible to separate these from one another. We cannot say, "I have faith, and therefore can live however I please" As though God's grace is an excuse for sin (Romans 6:1-2). Nor can we say, "I have works, therefore allow me to glory in what I have done". For it is by grace alone that we are saved, having been justified by God's grace on Christ's account, through faith alone.
Luther in his introductory notes to the Epistle to the Romans says that one can no more separate faith and works than one can separate heat and light from fire.
What is important is making the strong and hard distinction between Law and Gospel, between grace and commandments, between our justification and our sanctification.
Nothing we do can improve our status before God by even so much as by a Planck length. All that we have before God is what God Himself has freely given us. That does not mean we sit on our duff and womble about twiddling thumbs--it means we have a life to live here, one that is defined by Christ and His holy cross. A way to live, the Christian way, the way which Christ has instructed and taught us. That is to take up our cross and be Jesus' disciple.
To be Jesus' disciple is not just some status we can cozily inhabit; there is a daily call, "Take up your cross and follow Me", a multitude of moments happen every single day: Do we follow Jesus or do we ignore Jesus? A person just cut you off in traffic, someone was rude to you at work, you see a homeless person on the street corner that is hungry. Each day contains a day's amount of opportunities to follow Jesus or not follow Jesus. To be a follower of Jesus isn't just something we get to claim for ourselves without doing anything. Jesus' way is hard and difficult, but it's His way, and He is Lord.
Recall in Matthew 7, the Lord speaks of those who, on the Day of Judgment, will say to Him, "Lord, Lord" they will boast of their faith (as though they did that) and works, but the Lord will rebuke them saying, "I never knew you". There is a danger in being comfortable in ourselves; Christ invites us to rest in Him, to comfort us--so that our comfort might come from Christ, our confidence is found in Christ, our lives might be found in Christ--whether in living or dying, in joy or sorrow, in hardship or prosperity.
Such is why Christ says, "I am the Vine and you are the branches" for we can do nothing apart from Him, apart from Him we have no life and we wither and die.
Does that mean we must earn our keep? Heavens no.
Does that mean if we fail and stumble the Lord shall cast us away? No!
But it does mean that we must ever be on the receiving end of grace. The reason the Lord instituted the sacred ministry for His Church, by telling His apostles to preach forgiveness of sins, to preach the Gospel to every living creature, to make disciples baptizing them in the name of the Father, Son, and Holy Spirit; the reason why He instituted His Supper, the reason He gave all these gifts and ministry to the Church is in order that He ever be preached in the Church. To preach Law and Gospel, not confusing these; but recognizing that the Law is the Law, even though it is harsh and painful to hear it because of our sin; and that the Gospel is the Gospel, ever sweet and good news in the ear of the sinner whose sins are freely forgiven.
The word is preached, the word is declared, God brings us in by water, word, and Spirit, keeping us here by His grace, by word, and bread, and wine, and the Spirit. For wherever the Word is preached and the Sacraments administered, here is God. God who loves us, God who saves us, God who keeps us, God who strengthens us, God who comforts us, God who will not let us go.
To be a Christian is to live in Christ by faith, to live in our neighbor by love; to be defined and examined in every way by the Cross. For the cross tests and proves everything.
-CryptoLutheran