“For if you forgive others their trespasses, your Heavenly Father will also forgive you. But if you do not forgive others, neither will your Father forgive your trespasses.” (Matthew 6.14-15)
I would encourage you to not move so quickly to, “this verse is not talking about works righteousness. Your salvation is not dependent on forgiving others.”
Yes, no verse in the Bible commands Christians toward works-righteousness. So you must not forgive in order to be saved. But does that automatically mean that your salvation is not dependent on forgiving? Just depends on what you mean by “dependent” I suppose.
This text is pretty straightforward. So in order to not lose the clarity of Scripture, I would suggest hearing Jesus’ words in light of the doctrine of perseverance. Election is unconditional. But our calling is conditioned upon our election. Our justification is conditioned upon faith. Our sanctification is conditioned upon justification. And our glorification is conditioned upon perseverance. It is an unbreakable chain. It is all by grace through faith in Christ alone, for the glory of God alone. But I think if we understand the order of salvation in this way, we can remain Protestant, and also give due justice to each text.
It is in this context that I can say (along with Jesus), “if you forgive–if you persevere in a life of forgiveness– your Heavenly Father will also forgive you– God will grant you access to His glory on the final day.” It is actually only those who are bent toward works-righteousness who have to understand that sentence in a works-righteous way.
So as always, I would remind you, if you remember what Christ has accomplished for you already on the cross, then you will persevere.