Is there any sin that can't be forgiven?

Yes. This article answer: https://www.jw.org/finder?wtlocale=E&docid=5020161...

NO +×++×++++++++

Read 1 John 1:9  for your answer.

WHY DO WE NEED THE RANSOM? A ransom is the rice paid to release a person  from the threat of death. ( exodus 21:29,30) death and old age were not part of god's original purpose for mankind. How do we knw that? God told the first man, Adam, that if he committed what the Bible calls "sin," he would die. So if Adam had not sinned, he would never have died. ( Genesis 2:16, 17; 5:5) according to the Bible, death "entered" the world of mankind through Adam. Thus, Adam passed on to all his descendants sin and its penalty, death,. We need a ransom to release us from the penalty of death that we inherited from Adam. Read Romans 5:12; 6:23. Who could pay the ransom to free us from death? When we die , we pay the penalty only for our own sins. Read psalm 49:7-9.   WHY DID JESUS DIE? Unlike us, Jesus was prefect. So he did not need to die fore his sins- he never committed any. Instead, Jesus died for the sins of others. God expressed extraordinary love for mankind by sending his Father and giving his life for our sins. Read John 3:16; Romans 5:18,19. fore more information JW.ORG

Only unbelief. Believe and you will be forgiven and saved.

The only unforgivable sin is denial of the means of forgiveness; the Holy Spirit. Sin can be condensed down to three sources of all sin: "For everything in the world--the lust of the flesh, the lust of the eyes, and the pride of life--comes not from the Father but from the world." (1 Jn. 2:16)

As long as you're alive and you repent to God sincerely, God is all forgiving, all-pardoning and merciful.  As long as your soul is in your body, the Mercy of God, the Forgiveness of God and the Doors of God are open to you. Some people don't realize the beauty of God's repentance, God's mercy, God's kindness upon our souls and who loves to forgive.

The concept of "sin" (i.e. artificially providing both the sickness and the cure) is in itself an unforgivable sin.  Or in other words it's the concept of sin that is the problem because creating punishments around it and threatening people with hell if you don't follow artificial and arbitrary rules is immoral.

No, there isn’t.  God is love and not only forgives everything, he doesn’t hold anything against us in the first place.

The key is to repent