God has revealed Himself to man. He has revealed Himself both in natural revelation and special revelation. As much as we may think we know about God and as much as we may think we know theologically we must always keep in mind that the eternal God has only revealed a very small portion of Himself to us His creation. We have natural revelation to be sure, and we have 66 books in the canon of our Bible, but outside of that there is still much more that we would like to know. For now we must utilize what has been revealed and have faith that there is a reason for what has not been revealed.
The Trinity is one of those doctrines that the most honest theologian must admit that there seem to be at times many more questions than answers. We certainly have much revealed to us concerning the nature of the Trinity and a basic understanding of it and why it should matter to us. Just because we don't have a full understanding of the Trinity does not mean that we can't say that we do in fact know some things about it. Many want to say that because we don't know everything than we can't know anything. This is not accurate and apply that to everything in life and you will see why it is nonsense.
A basic definition of the doctrine of the Trinity is: There is one God eternally existing in three distinct persons. This is what would be called a basic Trinitarian view. There are other views out there concerning the nature of God that would be in opposition to this view including:
One way of putting it would be this way. All three persons including God the Father, the Son and the Holy Spirit are all equally God in all eternity. None are created beings and there was never a time where any of them didn't exist for they are all God. However, God the Father is not God the Son, God the Son is not God the Father, and God the Holy Spirit is not the Son or the Father, so on and so forth. This is true and it also remains at the same time that they all 3 are eternally and equally God Almighty.
Now, at this point I will be perfectly honest with you I don't have a full comprehension of this doctrine. My frail human mind can't wrap around the idea of how God could be one God and yet exist in three distinct persons. How they interact with One another and how they all remain at all times in perfect unity among other questions I may have. However, I don't have to know everything to believe something and I do believe the Bible is clear about the Trinity. So while I may not fully comprehend or can fully understand the inner workings of or the concept of how something like this is possible does not preclude my belief in it.
I believe that the doctrine of the Trinity is one of the fundamental doctrines of the historic Christian faith as taught in the 66 books of the Old and New Testaments of the Holy Bible. Now, let us get to the question at hand: "Must you believe in the Trinity?" Or to put it another way, "Do you have to believe in the Trinity to be saved?"
My short answer is obviously, "Yes!" Let me explain. In order to be saved one must believe that Jesus Christ was a real person, that He was God in human flesh, fully God and fully man, that He lived a sinless perfect human life, He died on the cross to make the payment for sin, and He rose from the dead on the third day. Jesus is the only sacrifice that God accepts as payment for sin and by placing my faith in Jesus for salvation and making Him Lord of my life I am regenerated, I am justified, I am saved, I have eternal life, and I have the indwelling Holy Spirit.
By definition salvation involved the Trinity. It involves God the Father who gave His Son to the world as a payment for sin. It involves God the Son who gave Himself as a ransom for sin, and it involves the Holy Spirit who comes to indwell believers are the moment of salvation.
Here is the thing though. Ignorance of a doctrine does not equal willful rejection of it. James White addresses this in the video I will link at the bottom. One can be saved and believe in Christ and understand that He is in fact God in human flesh and that He is the only payment for sin while maybe not fully understanding what the doctrine of the Trinity teaches or they may even have a differing view at the time.
James White makes the argument and I agree that most Christians by default many times end up being modalists. This is usually out of ignorance. Most, especially newborn babes in Christ who have simply not had enough time under sound doctrinal teaching usually lend towards modalism because in their minds it "makes the most sense" and since our pride usually dictates our beliefs at times it is hard to give up something believed that is easier to comprehend for something that is true but harder to comprehend.
So to believe in modalism does not necessarily prevent salvation because as I stated it may be held to at the time of salvation in ignorance to the true teaching of the Bible which is a trinitarian view. For instance, when I was saved at a very young age I did not know all that I do not about the Trinity and certainly could not articulate it to you, but I believed in Jesus and that He was God and that He could save me from my sin so I could go to heaven and that was all I needed to know at that moment.
However, there is a difference between ignorance and willful rejection. If one comes to understand or has been taught the biblical doctrine of the Trinity and then willfully rejects said teaching than to me that is a huge red flag as to the person's spiritual condition. If the Trinity was some unclear teaching or if it did not affect so many other doctrines then it may not be of so much importance. However, the doctrine of the Trinity fundamentally affects all other doctrines of the Bible because without the Trinity you don't have a God the Son who can save from sin. Without the Trinity you don't have a Holy Spirit that can indwell believers and point the sinner through conviction to Jesus Christ who is God the Son. Without God the Son you do not have a mediator between God and man and you do not have a payment for sin to make us justified and righteous before a holy God the Father.
So for one to come to be taught the doctrine and then willfully reject it and cling to a strict monotheistic belief like you see in Islam and other false religions, and for them to emphatically state that there is no Trinity then that would be a point of division between that person and other Christians based on the unity that exists between believers around the fundamentals of the faith.
A modalist, someone who thinks there is one God and just simply operates in different modes may hold to this to try and understand how a Trinity may be possible and may not actually willfully reject the idea or the teaching of the Trinity, but once they have been clearly shown that the doctrine of the Trinity does involved three distinct persons and that this is clearly taught then at that point if they willfully reject it then it becomes a matter of concern because they are rejecting what is a fundamental doctrine of the Bible.
I am going to link two videos for you on this topic. The first is a "Dividing Line" episode where James White responds to some material that was online concerning this subject. They other is a debate from 2011 between Dr. White and a Oneness Pentecostal view.