In James 5:20, the expression "shall cover a multitude of sins" means that the sins of the person who has strayed will be forgiven by God. The significance is that if the sinful person listens and repents, eternal punishment will be averted. Linked to this is Jude verse 23:
"Rescue others by snatching them from the flames of judgment." (NLT)
1 Peter 4:7-8 is cross-referenced to Proverbs 10:12 which says:
"Hatred stirs up dissension, but love covers over all wrongs."
The emphasis here is on how love promotes forgiveness.
However, because Protestants don't distinguish between "mortal" and "venial" sins, then no reference is made to any explicit sin. All sin is rebellion against God and the Protestant view is that there is only one sin that can't be forgiven by God and that is the sin of rejecting Christ Jesus as Lord and Saviour.
Edit for clarification: The Protestant view is that all sins are mortal sins in that even one sin makes the offender worthy of eternal separation from God.
Here is a summary of the Protestant view of justification and salvation as expressed by John Stott:
I have been saved – in the past – from the penalty of sin – by a crucified Saviour: “For in this hope we were saved" (Romans 8:24).
I am being saved – in the present – from the power of sin – by a living Saviour: "For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God" (1 Corinthians 1:18).
I shall be saved – in the future – from the presence of sin – by a coming Saviour: "Since we have now been justified by his blood, how much more shall we be saved from God's wrath through him!" (Romans 5:9)