categories of sin
As we pray for ourselves and for others for the forgiveness of sin, we need to take note of sin's categories.
In one sense, sin is sin. The Apostle John states that all wrongdoing is sin (1 John 3:17). There's really no lesser or greater. Left to itself, the wages of sin is always death (Romans 6:23). This happens either in the deadly consequences of sin in this life, including physical death itself, and in the more deadly consequences in the life to come, the second death of eternal separation from God. Thankfully, we're also promised that the gift of God is eternal life in Christ Jesus our Lord (Romans 6:23), offered to those who are in Christ by His Grace through repentant faith.
However, the Bible refers to an eternal sin (Mark 3:29) and a mortal sin (1 John 5:16), both leading to the second death. We're told not to ask God to forgive such sin.
Say what? I thought we always should be asking God to forgive us our sins and those of others, end of story. From The Cross, Jesus asked the Father to forgive those who sent Him there (and that would be all of us, BTW), and no doubt He's praying for our forgiveness at this moment in Glory as He lives to make Intercession for us at the Father's Side (Hebrews 7:25). And so, we too should be praying for everyone, in all circumstances, that they would come to Jesus to receive His Forgiveness of sin purchased for them on the Cross.
But the eternal sin Jesus speaks of in the Gospel of Mark is the kind of sin that disqualifies those who commit it. This is the sin of persistent unbelief, seen in those in Jesus' day who said of Him, "He has an impure spirit" (Mark 4:30). John says that those who don't care about the testimony that God has given about His Son make Him out to be a liar (1 John 5:10). (So if you're concerned about having committed this unforgivable sin, your concern is a sign that you haven't) Until and unless unbelievers repent and believe in Him Who has been sent to forgive sins and grant eternal Life, they have sealed their fate.
Therefore, in their case, we should adjust our prayer tactic. We should ask God, not to forgive their sin of unbelief, but to turn their hearts and minds towards The One Who died that they might repent, believe, and be forgiven by God, Who commands all people to repent (Acts 17:30), and Who wants all people to be saved and come to a knowledge of The Truth (1 Timothy 2:4).
The gateway to Forgiveness and Life is repentance, so let's ask God to enable us and others to walk through it.