Unless there is a cross, there is no rightness about forgiving sinners. But there is, on both counts.
God is "faithful AND just to forgive us our sin" (1 John 1.9). How in the world can God be just in forgiving sinners? How can He let murderers and rapists and abusers and hate-promoters and greedy and immoral and idolaters just go free? Can you imagine the outcry (especially in Texas, where I reside) if a judge just let some folks like that walk? He'd never make it out of the courtroom.
But here is God the Just, letting sinners (who have done all the above and worse) walk. How is that just? It's simple and ingenious. By Jesus Christ dying on the cross as our propitiation (1 John 2.2), God accomplishes both justice and justification (Rom. 3.26).
He accomplishes justice by punishing all of humanity's sin, once for all time in one place. Christ was able to bear the weight of that punishment because He is God's Son, the divine Lamb of God who takes away the sin of the world. He bore our sins in His body (1 Peter 2.24) and became sin for us (2 Cor. 5.21) in order that God might have one sacrifice count for all, thus absorbing the blow of God's just wrath.
God accomplishes justification by counting Jesus' sacrifice as adequate for all who put their trust in Him, ceasing from their self-justification before God. What's more, everyone who has confidence in Jesus' sacrifice is forgiven and counted righteous in Christ. It's not just that the guilty are set free, but that God counts Jesus' obedience to Him as our obedience to Him. Amazing.
And some these days call this cosmic child abuse. Some call it pathetic and small. Some call it brutal and primitive. The Bible calls it the Gospel. He died that we might live. Amen.