What do Orthodox Christians believe about salvation?
This was a hard concept for me when I came to Orthodoxy. People don't realize the Reformers were presenting answers to Catholicism. The whole faith and works debate of the 16th century is not historical Christianity, and the Reformers were misreading St Paul. How do I know? Because nobody read St Paul like that previously. That's why Luther and Calvin don't refer to the Church Fathers.
Salvation is the path of becoming like Christ, and at the end of that path is our death and our judgment from Christ. Christ says in the gospel, many will come to me on that day and say, Lord, Lord, we knew you, and I will say, I never knew you. So proclaiming your salvation as if you know you're saved and nobody can take it away directly contradicts the words of Christ.
Salvation is a journey with Christ, becoming like him, which involves both our faith and trust in him and an active life that reflects the gospel. St Paul says to hand over the brother living in sexual immorality, he doesn't call him saved. And Christ in the first chapters of Revelation tells the churches, you believe, but you need to correct your lifestyle. That is the teaching of the Bible.
Matthew 7:21-23 · 1 Corinthians 5:5 · Revelation 2:1-3:22

