This post is a twist on the much more common question of “is the old testament relevant?” As far as I know, nobody has ever asked whether the new testament is relevant to Christianity. Let me rephrase the question: what would Christianity need in order to survive intact if the new testament were lost?
In the study on the important parts of the life of Jesus, there were a few points that were critical, mainly, that Jesus was the Jewish Messiah. He took on the four roles of prophet, king, priest, and sacrifice. Of these only the latter was completely unexpected and yet the most important. It is critical, therefore, that the story of Jesus’ sacrifice and resurrection supplement the OT. Without this, there is no Christianity.
A bit of history is therefore required to explain how the death and resurrection of Jesus was sufficient to wash away sins, but this information is historically explanatory in nature, not sacred in a doctrinal way. Indeed, if the NT were to be lost, we would want to be able to reconstruct the historical context and keep some measure of the historical narrative so that we could make sense of it all.
That’s it. If you have the OT, the knowledge that Jesus was the Jewish Messiah, that he fulfilled the roles of prophet, king, priest, and sacrifice, along with enough historical context and narrative, you have enough to build Christianity.
Let’s look at some of the core teachings of Christianity that come out of the NT:
Jesus taught that salvation required an act of recognition of sin and repentance. But the OT already taught that salvation came from repentance and sacrifice. The only difference is that Jesus became the final sacrifice and that faith in Jesus led to salvation. This information is covered by the minimal replacement NT.
2) Moral Code
We would certainly be poorer to lack the clarity of the teachings of the Sermon on the Mount (Matthew 5-7), but Jesus derived all of these teachings from the OT principles. The same goes for many other teachings. He didn’t change the moral codes of the OT, he just clarified them. The holy living requirement, from the OT to the NT, has never changed.
Jesus identified the greatest commandments in the law (the OT) as loving God and loving others. Jesus just pointed out what was already there.
Want to know about the end-of-times? Well Jesus didn’t change that. The OT always promised that the Messiah would come at the end-of-times to take everyone to final judgment. They just didn’t know that Jesus had to come to be a sacrifice first. Even though the replacement NT doesn’t contain any information on what happens at the end-of-times, that isn’t important. All that matters is faith: trust that God will keep the promises he made in the OT. Jesus didn’t change those, and you really don’t need to know the play-by-play at the end of days. You’ll get by without that knowledge.
5) Heaven and Hell
Along with eschatology, knowing what happens after you die is unimportant. Knowledge of salvation is sufficient. Trust God for the rest. Details are nice, but you really don’t require them.
Is the NT relevant?
Of course parts of the NT are important, as stated above. But the vast majority is optional. The complete OT and a key summary of the NT is sufficient to maintain Christianity. Why? Because unlike all the other world religions that have ever been, God chose to interact with his people through relationships, not yet-another-holy-book. That’s why he never gave us a new canon. Humans councils came up with those.
Christianity lives in the people: not a book, not an organization, not a building, nor doctrines, nor a history. This is the genius of God revealing himself; to do so in relationships multiplied in the lives of his followers. It is the Christian life lived out for all to see.
That is why Christianity would survive even if the sacred cow doctrines of various denominations fell because the NT were lost. God’s message to humanity and the love of his followers does not rely on a book. It relies on the living example of its followers.
Am I saying the NT is unimportant? No. It provides clarity and makes finding God a whole lot easier. But sometimes we over-complicate things. Jesus was all about actions. Repentance, living a holy life, and loving. It was never about rote doctrinal expression, which is why only two ritual were mandated: baptism and communion.
 Presumably because it is an incredibly stupid question.