Are there any Christian sects that say salvation is based, in whole or in part, on your response to Jesus on Judgment Day?

The various "New Church" denominations that follow the Christian teachings and Bible interpretations written by Emanuel Swedenborg (1688-1772) have a view of salvation that is partially, though not wholly, compatible with the salvation theory that your Christian friend describes.

Key points that are compatible:

• Non-Christians and people with faulty or false conceptions of God can be saved.
• Those who are saved will accept God, and most of them will accept Jesus Christ as God, during their preparation for heaven in the afterlife.
• In the afterlife we are not punished for any evil actions done on earth; only for evil actions we continue to commit in the spiritual world.

A key point that is probably incompatible:

• It is through the decisions we make and the life we live on earth that we develop a character that either will or will not accept God's lordship in the afterlife, and that either will or will not continue to commit evil actions in the afterlife.

I should add that in Swedenborg's theology there is not a single Judgment Day on which all people are simultaneously judged, but rather each person faces his or her own particular "judgment day" as part of a step-by-step process that begins immediately after each individual's death.

Here are a few sample quotations from Swedenborg's writings in which he makes the above points.

About non-Christians and people with faulty ideas of God being saved:

It is an insane heresy to believe that only those born in the church are saved. People born outside the church are just as human as people born within it. They come from the same heavenly source. They are equally living and immortal souls. They have religions as well, religions that enable them to believe that God exists and that they should lead good lives; and all of them who do believe in God and lead good lives become spiritual on their own level and are saved, as already noted.

Someone could point out that they have not been baptized. But baptism saves only people who have been spiritually washed, that is, regenerated. Baptism serves as a symbol and reminder of this.

Someone could point out that they do not know the Lord, and that apart from the Lord there is no salvation. But no one is saved because of knowing about the Lord. We are saved because we live by his commandments. Further, the Lord is known to everyone who believes in God because the Lord is the God of heaven and earth, as he tells us in Matthew 28:18 and elsewhere.

Particularly, people outside the church have more of a concept of a personal God than Christians do; and people who have a concept of a personal God and lead good lives are accepted by the Lord. Unlike Christians, they believe in God as one in both person and essence. Further, they think about God as they lead their lives. They treat evils as sins against God; and people who do this are thinking about God as they lead their lives. (Divine Providence #330)

About people accepting God, and commonly accepting Jesus Christ ("the Lord," in Swedenborg's terminology) as God in the afterlife if they had not been Christians or had not had a clear idea of God in their earthly life—provided that they had lived a reasonably good and thoughtful life on earth:

I have been taught by a great many instances that if non-Christians have lived decent lives, intent on obedience and appropriate deference and in mutual thoughtfulness as their religion requires so that they have acquired a measure of conscience, they are accepted in the other life and are taught by angels about matters of goodness and truth with most sensitive care. Once they have been taught, they behave unpretentiously, intelligently, and wisely and readily accept and absorb truths. This is because no false principles have taken form to oppose truths of faith, principles that would need to be ousted, let alone slanders against the Lord, as is the case for many Christians whose treasured concept of the Lord is simply of an ordinary human being. It is different for non-Christians. When they hear that God became a person here and made himself known in the world, they acknowledge it immediately and revere the Lord. They say that of course God made himself known; after all, he is the God of heaven and earth, and the human race belongs to him.

It is a divine truth that there is no salvation apart from the Lord, but this needs to be understood as meaning that there is no salvation that does not come from the Lord. (Heaven and Hell #321)

About our not being punished for evil actions done on earth, but only for evil actions we continue to do in the afterlife—and yet that the choices we make on earth, and the life we live pursuant to those choices, determines whether we will continue to commit evils in the afterlife ("the world of spirits" is Swedenborg's term for the region of the spiritual world that everyone enters after death before going to his or her final home in either heaven or hell):

Since evil spirits plunge into all kinds of evils when they are in this second state [after death], it is normal for them to be punished often and severely. There are many kinds of punishments in the world of spirits, and there is no respect for rank, for whether someone was a king or a servant in the world. Every evil brings its own punishment with it. They are united; so whoever is involved in something evil is involved in the punishment of the evil as well. Still, no one suffers any punishment for evil things done in the world, only for current evil deeds. It boils down to the same thing, though, and makes no difference whether you say that we suffer punishments because of our evil deeds in the world or that we suffer punishments because of our evil deeds in the other life, because after death we all return to our life, which means that we are involved in the same kinds of evil. This is because our nature is determined by the kind of physical life we led.

The reason they are punished is that fear of punishment is the only means of taming their evils in that state. Encouragement does not work anymore, or teaching or fear of the law or fear for their reputation, because they are acting from their nature, which cannot be compelled or broken by anything but punishments.

Good spirits are never punished, though, even though they have done bad things in the world. This is because their evils do not come back. I have also been granted a knowledge that their evils are of a different kind or nature. They do not stem from any deliberate resistance to what is true, and they are not from any evil heart except the one they acquired by heredity from their parents, which blind pleasure drove them into when they were involved in outward concerns separated from inner ones. (Heaven and Hell #509)

In other words, according to Swedenborg, regardless of what religion people had belonged to or what they had believed about God here on earth, they will be given the opportunity in the afterlife to learn the true nature of God, and what it truly means to live a good and heavenly life. If at that point they are willing to learn, to accept God, and to live a good, moral, and spiritual life, then they are accepted into heaven. No faulty beliefs held or wrongful actions done on earth will be held against them, since their intent was and is to live a good and thoughtful life, which they now recognize comes from God.

This much is compatible with your Christian friend's belief.

However, according to Swedenborg it ultimately is the choices people make on earth, and the life they live according to their own choices and beliefs, that will determine whether in the afterlife they are willing and able to accept true teachings about God and spiritual life, and therefore go to heaven. If they are ultimately more interested in their own self-interest, pleasure, power, and so on than they are in loving and serving God and their fellow human beings, then they will reject God, the truth, and spiritual life when it is offered to them, and will choose instead to spend eternity in hell.

For more on these points based on Swedenborg's theology, please see these articles:

• If there’s One God, Why All the Different Religions?
• Is Jesus Christ the Only Way to Heaven?
• What Happens To Us When We Die?
• Is There Really a Hell? What is it Like?