Certainly, you can be mentally ill and a Christian. But being a Christian and staying mentally ill doesn't seem to square with what Scripture describes of the Christian life:
2 Timothy 1:7
7 For God has not given us a spirit of fear, but of power and of love and of a sound mind.
Galatians 5:22-23
22 But the fruit of the Spirit is love, joy, peace, longsuffering, kindness, goodness, faithfulness,
23 gentleness, self-control. Against such there is no law.
1 John 4:15-19
15 Whoever confesses that Jesus is the Son of God, God abides in him, and he in God.
16 And we have known and believed the love that God has for us. God is love, and he who abides in love abides in God, and God in him.
17 Love has been perfected among us in this: that we may have boldness in the day of judgment; because as He is, so are we in this world.
18 There is no fear in love; but perfect love casts out fear, because fear involves torment. But he who fears has not been made perfect in love.
19 We love Him because He first loved us.
Philippians 4:6-7
6 Be anxious for nothing, but in everything by prayer and supplication, with thanksgiving, let your requests be made known to God;
7 and the peace of God, which surpasses all understanding, will guard your hearts and minds through Christ Jesus.
Matthew 11:28-30
28 Come to Me, all you who labor and are heavy laden, and I will give you rest.
29 Take My yoke upon you and learn from Me, for I am gentle and lowly in heart, and you will find rest for your souls.
30 For My yoke is easy and My burden is light."
Romans 14:17
17 for the kingdom of God is not eating and drinking, but righteousness and peace and joy in the Holy Spirit.
And so on.
How is it that a man who has the Spirit of the Almighty God of the universe within him and who Scripture promises will bring peace, and joy, and freedom from fear remain embroiled psychologically in fear and depression? Is Scripture lying to us? Is God not strong enough to fulfill His promises to us of an abundant life, a life of rest, and peace, and joy?