Acts 16:31 states
They replied, “Believe in the Lord Jesus and you will be saved, you and your household.”
And Acts 10:43 says,
About him [Jesus] all the prophets testify, that everyone who believes in him receives forgiveness of sins through his name.
Similarly, John 3:16 says
For this is the way God loved the world: He gave his one and only Son, so that everyone who believes in him will not perish but have eternal life.
And John 3:36 states,
The one who believes in the Son has eternal life. The one who rejects the Son will not see life, but God’s wrath remains on him.
Likewise, Mark 16:15-16 states,
He said to them, “Go into all the world and preach the gospel to every creature. The one who believes and is baptized will be saved, but the one who does not believe will be condemned.
Because of these verses, belief in Jesus Christ is widely regarded as a requirement for salvation, and the biblical basis arises from the interpretation of what, exactly it means to "believe" in Christ. This statement in Acts 16:31 and similar statements throughout the Bible make what you believe about who Christ said he was extremely important. In Knowledge of the Holy, A.W. Tozer frames it this way, (pg 5)
Among the sins to which the human heart is prone, hardly any other is more hateful to God than idolatry, for idolatry is at bottom a libel on His character. The idolatrous heart assumes that God is other than He is - in itself a monstrous sin - and substitutes for the true God one made after its own likeness. Always this God will conform to the image of the one who created it...
Not all who called themselves Christians through the centuries were Trinitarians, but as the presence of God in the fiery pillar glowed above the camp of Israel throughout the wilderness journey, saying to all the world, “These are My people,” so belief in the Trinity has since the days of the apostles shone above the Church of the Firstborn as she journeyed down the years. Purity and power have followed this faith. Under this banner have gone forth apostles, fathers, martyrs, mystics, hymnists, reformers, revivalists, and the seal of divine approval has rested on their lives and their labors. However they may
have differed on minor matters, the doctrine of the Trinity bound them together.
This, however, is the real Christian faith, that we honor one
single God in three Persons and three Persons in one single Godhead..
this tenet of the ancient creed has been held by the Eastern and
Western branches of the Church and by all but a tiny minority of Christians.
And for this reason, belief in the Trinity is not just important, but is required for salvation. If Jesus really claimed to be God, then If one does not believe that Jesus was a member of the trinity, a part of the triune Godhead, then one does not actually believe in Jesus or his claims. Instead they believe in an idol of their own making, for it is clear in scripture and it has been clear throughout history to so many theologians that Jesus claimed to be God. As St. Thomas Aquinas said in Nature and Grace,
Explicit belief in the Trinity has therefore been necessary for salvation from the very beginning. ...it is impossible to believe explicitly in the mystery of the incarnation of Christ without faith in the Trinity. For the mystery of the incarnation of Christ includes that the Son of God took flesh, that he made the world new through the grace of the Holy Spirit, and that he was conceived by the Holy Ghost.