The Catholic and Protestant traditions revere the Lord Prayer, which says in part:

Matthew 6:12

"And forgive us our debts, as we forgive our debtors."

Immediately after telling His disciples to pray that way, Jesus gives us more details about forgiveness:

Matthew 6:14-15

"For if you forgive men their trespasses, your heavenly Father will also forgive you. But if you do not forgive men their trespasses, neither will your Father forgive your trespasses."

In other words, Christians are to forgive others if they wish God to forgive their own offenses. (Jesus was emphatic on this point when He explained about forgiveness with the Parable of the Unforgiving Servant in Matthew 18:21-35.)

I have not seen any literature where the Catholic and Protestant perspectives differ in this regard when they are talking about this passage of Scripture.

A Catholic Understanding

There are two parts to your question:

• Can one forgive another for a wrong they have not suffered personally?
• Can one forgive another if God has not forgiven them?

One at a time.

Can one forgive another for a wrong they have not suffered personally?

If one hasn't suffered a wrong personally, it's not clear that there's anything to forgive, or be forgiven, in a technical sense. I might feel outraged as a Catholic by the way Catholics have historically been treated, or as an Irish citizen (at least technically) by the way the Irish have often been treated; but that doesn't mean there's anything for me to forgive. I am required to live in charity with my neighbor, however; and to that extent I may be said to "forgive" someone if I put aside my anger at them (an anger I have developed on behalf of another) and dwell with them in peace. Indeed I must do so:

When you stand to pray, forgive anyone against whom you have a grievance, so that your heavenly Father may in turn forgive you your transgressions.

(Mark 11:24)

Can one forgive another if God has not forgiven them?

From a Catholic perspective, there are a few things to be addressed here. First of all: Should one forgive a person who does not appear to have sincerely expressed repentance? Second: Assuming that someone has expressed what appears to be sincere repentance, is it possible that God does not forgive them? Finally: is it possible, or morally right, to forgive someone whom God does not forgive? Let's take those individually.

• Should one forgive another who has not sincerely repented?

In his discussions of forgiveness, Jesus nowhere appears to put conditions.

Then Peter approaching asked him, "Lord, if my brother sins against me, how often must I forgive him? As many as seven times?" Jesus answered, "I say to you, not seven times but seventy-seven times."

(Matthew 18:21–22; New American Bible, Revised Edition)

The NABRE note to this text points out the similarity to Genesis 4:24, and notes:

In any case, what is demanded of the disciples is limitless forgiveness.

Further, the Catechism of the Catholic Church (in the context of its discussion of family life) states:

Each and everyone should be generous and tireless in forgiving one another for offenses, quarrels, injustices, and neglect. Mutual affection suggests this. The charity of Christ demands it.

(paragraph 2227)

Thus, it appears that from a Catholic perspective, yes; one should and indeed must forgive another regardless of whether they have repented or not.

• Assuming that someone has sincerely repented, is it possible that God does not forgive them?

No.

"There is no one, however wicked and guilty, who may not confidently hope for forgiveness, provided his repentance is honest."

(Catechism of the Catholic Church, paragraph 982, quoting the Roman Catechism, Part I, chapter 11, paragraph 5)

• Is it possible, or morally right, to forgive someone whom God does not forgive?

We can never know for certain whom God has forgiven, and whom he has not. God is not bound by his Sacraments, and has many ways of forgiving, even up to the point of death. Further, we have the two prior statements: that we must forgive others regardless of circumstances, and that God will forgive one who sincerely repents.