What is the Protestant view of John 20:23 and the disciples ability to forgive sins?

Christians are called to follow in the footsteps of Jesus.

Simply put, disciples learn at the feet of the teacher so that they can go out and do what the teacher does. As Christians, we are called upon to act in the manner of Christ, and in so doing, assume His authority. That includes the forgiveness of sins. As this verse shows, we are given the authority to forgive sins, as Jesus does. As Matthew 6:14-15 shows, we are also called upon to forgive all those who sin against us, as Jesus does:

For if you forgive other people when they sin against you, your heavenly Father will also forgive you. But if you do not forgive others their sins, your Father will not forgive your sins.

I will give a Lutheran view, in which both private & public confessions occurs with absolution. The former is done most often in private counseling sessions where inner (emotional) healing needs to occur. Although, there are also Lutheran churches that set aside time for private confession and a few even have confessional booths.

In the Augsburg Confession, the official position of the Lutheran church states:

... private absolution should be retained and not allowed to fall into disuse.

On a typical Sunday morning, following a time of public confession, a Lutheran pastor will say the following:

As a a called & ordinated minister...I (announce) forgive you all your sins in the name of the Father, Son & Holy Spirit.

Note that the words are not "may you be forgiven" or "we forgive you." Rather, it is an unconditional focus on the objective grace of forgiveness proclaimed through the spoken word.

In the Lutheran view of the Rite of Absolution, the pastor is acting persona Christi in proclaiming God's forgiveness. The reception of the Word of forgiveness is independent of how one feels and is not dependent on how well a person owns up to their shortcomings. Psalm 19:12 states: "Who can understand his errors?" The Lutheran Augsburg Confession states:

Our churches teach that private absolution should be retained in the churches, although listing all sins is not necessary for Confession. For, according to the Psalm, it is impossible. "Who can discern his error?"

The Lutheran theologian, George Stoeckhardt, writes:

A believing Christian does not make the pulse of his faith-life the criterion of his state of grace... The believer rather makes this conclusion: O, how godless I still am. Out of my heart godless thoughts continue to arise. There is no doubt but that I am a poor, unworthy sinner. My sin is ever before me. But now God’s Word tells me, that God has already declared godless Sinners righteous. Thus I belong without any doubt whatsoever in the number of those whom God justifies (St. Römerbrief, p. 185).

The focus of absolution in the Lutheran tradition is that, in confession, the penitent makes an act of contrition and the pastor acting in persona Christi announces the formula of absolution.

It's like having the charismatic gifts of healing and being prompted by the Holy Spirit to speak forth to that person in need, "be healed in the name of Jesus." This is why in the Lutheran tradition the laying on of hands often occurs at the same time as private absolution is given.

The proclaimed Word of God does the work of inner healing. In absolution there is not only an impartation of the Holy Spirit to work forgiveness, but healing gifts (including deliverance) are given as well. That is why Martin Luther said, "...where sins are forgiven, there is life and salvation as well."

Martin Luther once observed:

To be convinced in our hearts that we have forgiveness of sins and peace with God by grace alone is the hardest thing.

Luther also writes:

Sins are forgiven in two ways: First, sin is driven out of the heart and grace is poured in; only God does this. Second, the forgiveness of sins is proclaimed; one man does this to another. Christ, however, does both: He puts the Spirit into the heart and outwardly proclaims it with words. This is a proclamation and public preaching of the inward forgiveness.

Jesus says, "if you withhold forgiveness from any, it is withheld.” In the Lutheran tradition, if people don't want to confess their need for God's salvation, that is their problem. It's not like a pastor is saying "go to hell" to all those who don't confess. Rather, people who reject God's forgiveness self exclude themselves on their own from God's reconciling grace of having life in His presence.

Luther's little comment at the end of his exhortation to Confession in his Large Catechism defines the Rite of Confession & Absolution in terms of grace:

If you were a Christian then you ought to be happy to run more than a hundred miles to Confession and not let yourself be urged to come. You should rather come and compel us to give you the opportunity. For in this matter the compusion must be the other way around: we must act under orders, you must come into freedom. We pressure no one, but we let ourselves be pressured, just as we let people compel us and administer the Sacrament. (LC V. 30-31)

This is from a footnote in my ESV Bible and I trust it represents the majority protestant position on this verse.

The expressions they are forgiven and it is withheld both represent perfect-tense verbs in Greek and could also be translated, "they have been forgiven" and "it has been withheld," since the perfect gives the sense of completed past action with continuing results in the present. The idea is not that individual Christians or churches have authority on their own to forgive or not forgive people, but rather that as the church proclaims the gospel message of forgiveness of sins in the power of the Holy Spirit (see v. 22), it proclaims that those who believe in Jesus have their sins forgiven, and that those who do not believe in him do not have their sins forgiven--which simply reflects what God in heaven has already done.