Does a person need to have the "correct" doctrine to be saved?
Or, as pertains to this topic specifically...
Does a person need to be a Trinitarian to be saved?
(if you haven't answered that already)
Of course not. Both Jesus and Paul seemed to see the difference to be what I'd call an orientation. Jesus spoke of followers, and "sinners." Paul spoke of faith. Both, I think, speak of a person's basic direction. Not perfection. (Jesus used "sinner" to indicate an orientation. In a more literal sense we're all sinners, but that's not what he meant.)
Jesus used a child as his example of someone with the right orientation. Probably because children, when in proper families (which too many are not) instinctively trust their parents and want to be like them. None of this suggests that salvation is about holding the right beliefs.
Beliefs can matter. If you think the world is run by a vindictive God, you can develop into a person who hates everyone around you. There can also be political implications. So errors can cause problems. But I see no evidence in the NT that denying the Trinity damns anyone unless it results in the kind of person who is opposed to Christ’s teaching.
When I look at forums such as Christian Advice I see lots of people whose lives are close to ruined by theological errors, although I hope that they are not actually damned. I see in the world as a whole many religions and philosophies that I think place their members at great risk. Some of these, unfortunately, are Christian and even Trinitarian. I think theology is important, and spend a lot of time thinking and writing about it. But that doesn’t mean that God throws people with erroneous beliefs into hell.
To my knowledge, the NT passages about belief are really talking about faith, and faith should be understood in the Pauline sense of trust in God and commitment to God’s purposes, not in an abstract intellectual sense.
If you’re read my posting on this topic, you’ll know that I don’t even think one has to be a Christian. I think Christ was the Logos made flesh. But the Logos has worked in other ways, e.g. inspiring the prophets. In Rom 2 Paul implies that the Law (one form of the Logos, in Jewish understanding) was sometimes implanted in the hearts of even pagans. So I think when the Bible says that salvation comes only through Christ, it is including these various forms in which the Logos works. Abraham surely didn’t believe in three hypostases with one ousia, and likely didn’t even understand the distinction between Father and Son, although all three Persons were surely at work with him.