How do Nontrinitarians justify accepting the canon of Scripture but rejecting the Trinity?

Essentially as an EXtrinitarian, this is an basic question to answer.

The canon is a complete body of evidence God has provided which is without error or contradiction. If God inspired the entire work as 2 Tim 3:16 tells us, then there can be no confusion unless man has added it. We also know there are many additions and as some call them, corruptions, which have a trinitarian bias. These are easy to identify once you know what you are looking for. All trinitarian adjustments leave contradictions as evidence.

When one analyses trinitarian doctrine and compares to scripture we can readily see irreconcilable problems. Trinitarian doctrine is not biblically based, and has little biblical relevance. Any it claims to have is based on adjusted scripture or poor translations. There are many other ideas that have been devised that are not bible based like immortal souls and eternal punishment to name a couple.

It easy to accept the canon because it makes perfect sense and does not contradict itself. Trinitarian doctrine however is not like this at all. It doesn't make any sense and if one asks difficult questions, 'it's a mystery' is the usual response. The bible mystery is meant to be understood, God is meant to be understood because Jesus came to explain him.

TLDR: Canonical scripture was written by prophets of God, not by the Catholic church. The Creeds and concept of the Trinity were not written by prophets of God.

Your question is somewhat anachronistic. The books of the Old and New Testament did not become canon at the time of the creeds. These books and scrolls existed as canonical writings LONG before the creeds (as did many others which have been lost). Jerome merely compiled, organized and translated them. The books he eliminated (Apocrypha) are still read and studied by other denominations, but not necessarily universally accepted as canon by all non-trinitarian sects.

"We believe all that God has revealed, all that He does now reveal, and we believe that He will yet reveal many great and important things pertaining to the Kingdom of God. (Articles of Faith)"

The canonical books selected by Jerome when he first compiled the Vulgate were the remnants of the written words of prophets; all that God has revealed, or rather what remained of what he had revealed; True revelation by true prophets that survived the deaths of their authors and the fall of empires.

At the time of the protestant movement, there weren't exactly a lot of other codices floating around to re-compile a new collection of scripture, and the first mass-produced protestant bible was the KJV, which was essentially an English translation of the Catholic bible. They used the original Greek and Hebrew to retranslate the books, but they kept the same book organization and structure as the Vulgate.

The heresy of the trinity however was not the doctrine of God. It was invented by the apostate creeds of men who rose to power out of the fall of Christ's church. Modern revelation—what He does now reveal—has reaffirmed that Jesus is God the Father's literal son, and that we are God's literal spirit children.

It is not my intent to offend by speaking bold truths, but diminishing God's relationship between Him and His children by insinuating he is only figuratively our father, when he is in fact literally the father of our spirits completely undermines the purpose of our existence.

Let's start with the Old Testament. Why would Unitarians Christians reject those? They have very similar grounds for accepting them as Trinitarian Christians. There's really no difference there.

Now let's move to the New Testament. Although these were canonized relatively late, the same documents were held to have authority in the very early church. Why would you reject an account of Jesus' ministry by his disciple Matthew? Or John? Or a companion of Peter's or Paul's? Why would you reject Paul's letters?

The reason for accepting these texts isn't because certain people decided relatively late in the church's history to make them official. It's because the texts, in and of themselves, have authority. The canonization just reflects that, it doesn't cause that.

Q. What if, say, the Gospel of Matthew wasn't actually written by Matthew? Wouldn't you then have no reason to trust it?

A. The Gospel of Matthew gained, AFAWCT, almost universal authority in the very early church. So again, leaving aside the question of authorship, the text had authority well before becoming canon. The canon reflected that, it didn't cause that. So yes, we're inferring good reasons for authority re, say, the Gospel of Matthew - the description of events was considered credible very early on and almost universally. If there weren't good reasons for trusting the Gospel of Matthew, would it matter if it were canonized? No.

Most nontrinitarian groups are somewhat "on the fringes" of Protestantism (for the very reason that they reject the Trinity doctrine), and a few even deny that they are either Protestant or Catholic. This question seeks to explore a possible logical inconsistency in them accepting the canon of books of the Bible as held to by various church councils, yet rejecting council decrees that upheld the Trinity doctrine.

I would suggest that the canon of scripture has almost nothing to do with the nontrinitarian stance of rejecting church councils that upheld the Trinity doctrine. Nontrinitarian groups that seek to go by the Bible would say that all the books of the Bible that Protestants acclaim were also acclaimed by all first and second century Christians.

Another point that is worth mentioning here is that Catholics, Orthodox, and Protestants are agreed on the doctrine of the full deity and uncreatedness of the Father, the Son and the Holy Spirit. (Yes, there is argument with some on meanings of some words used in creeds about the Trinity, but they are all agreed on the Trinity doctrine as such.) Despite some differences about the worth of some documents, so that Protestants have a more restricted view on what documents are inspired of God, none of that affects the Trinity doctrine, for all the biblical support needed for it is found in the more restricted canon. The deutero-canonicals and later 1st and 2nd century writings that some think are also scripture do not contribute to the Trinity doctrine, so that is why the canon is not the issue here.

Their justification for rejecting the Trinity doctrine is based on two main points: their interpretation of scripture, and their belief that pagan ideas began to infect the early Christian Church, eventually leading to the Trinity doctrine. That latter view can be shown to be wrong, simply by examining the history of the early Church, gnostic and pagan influences, and how belief in the deity of Christ was understood as biblical way back from earliest Christian times, even though formal language about it took time to develop into its finished form. It's worth noting that the efforts of some individuals in the Church to bring in gnostic and pagan ideas caused formal wording of the Trinity doctrine to become necessary.

It's also worth noting that if groups interpret the scriptures to mean that the one it calls the Word of God, the one who is identifed as the Word made flesh (as the man, Jesus Christ), was created, then they will never, ever accept the Trinity doctrine. A created Christ would be a creature, inferior to God, having a starting point in time. That is why the wording of the Trinity doctrine excludes that notion. Those who say "There was a time when [Christ] was not", are anathemised by the Church, as some of their early creeds state.

I hope this helps clarify the real issues at work here.