Do any trinitarian Protestant traditions teach that anyone who denies the Trinity is necessarily unsaved?

While this statement may not have been made explicitly by any denomination, it can be established trasitively. In mathematics, the transitive property of equality is simply

If A=B and B=C, then A=C

Analogously, if Protestantism accepts Catholic teachings, doctrine, philosophy and scholarship throughout the ages regarding the Trintiy and Catholicism believes that you must believe in the doctrine of the Trinity for salvation, then Protestantism does as well.

Significance of the the Trinity in Protestantism

Within Protestantism, the trinity is nearly universally professed. For example, This doctrine was extremely important in the theology of Martin Luther, the initator of the Protestant movement. In his dissertation, "The doctrine of the Trinity in the hymns of Martin Luther" Dr. Paul John Grime explores Martin Luther's views on the Trinity vis-a-vis his hymns. From the Abstract:

While the doctrine of the Trinity was central to Luther's whole theological system, little attention has been paid to it. Most significantly, much of the research on Luther's theology has failed to note that Luther's well-known teaching on justification by faith was firmly grounded in his trinitarian thought. In order to investigate this matter, I chose to examine Luther's Trinity doctrine as it is presented in his hymns.

...

My examination of Luther's Trinity doctrine revealed a teaching that had much in common with the early church's dogma, especially its strong soteriological slant. Luther had a strong desire, however, to present the reformation teachings in a simplified form that could be grasped by the common person. This was clearly evident in his hymns, where Luther used simple language to convey a rich and vibrant teaching on the doctrine of the Trinity.

...

My conclusion affirmed my thesis, namely, that Luther's hymns do contain a doctrine of the Trinity that faithfully reflects that doctrine as presented in his other writings. Furthermore, I concluded that the hymns served well as a vehicle for proclaiming the reformation teachings, including the doctrine of the Trinity.

As such, Article I of the Augsburg Confession of the Lutheran Church states

Our Churches, with common consent, do teach that the decree of the Council of Nicaea concerning the Unity of the Divine Essence and concerning the Three Persons, is true and to be believed without any doubting; that is to say, there is one Divine Essence which is called and which is God: eternal, without body, without parts, of infinite power, wisdom, and goodness, the Maker and Preserver of all things, visible and invisible; and yet there are three Persons, of the same essence and power, who also are coeternal, the Father, the Son, and the Holy Ghost. And the term "person" they use as the Fathers have used it, to signify, not a part or quality in another, but that which subsists of itself.

Similarly, the 1689 Baptist Confession of Faith states in Chapter 2.

In this divine and infinite Being there are three subsistences, the Father, the Word or Son, and the Holy Spirit. All are one in substance, power, and eternity; each having the whole divine essence, yet this essence being undivided. The Father was not derived from any other being; He was neither brought into being by, nor did He issue from any other being. The Son is eternally begotten of the Father. The Holy Spirit proceeds from the Father and the Son. All three are infinite, without beginning, and are therefore only one God, Who is not to be divided in nature and being, but distinguished by several peculiar relative properties, and also their personal relations. This doctrine of the Trinity is the foundation of all our communion with God, and our comfortable dependence on Him.

Furthermore, the Westminster Confession of Faith states in Chapter 2.

In the unity of the Godhead there be three persons, of one substance, power, and eternity: God the Father, God the Son, and God the Holy Ghost: the Father is of none, neither begotten, nor proceeding; the Son is eternally begotten of the Father; the Holy Ghost eternally proceeding from the Father and the Son.

In Jesus and the Father: Modern Evangelicals Reinvent the Doctrine of the Trinity Dr. Kevin Giles makes clear the importance the Trinity in Evangelicalism:

In the past thirty years there has been an amazing resurgence of interest in the doctrine of the Trinity. Roman Catholics, mainline Protestatns, and Eastern Orthodox theologians have published numerous studies and books on the Trinity, and tey are continuing to appear. Evangelicals at first were not involved, but a change is under way, as this book and otherw written recently by evangelicals indicate.¹ After a long period of neglect, this doctrine is now on center stage as it should be, because it is nothing less than our distinctive Christian doctrine of God.

¹ For example, Millard Erickson, God in Three Persons: A Contemprary Interpretation of the Trinity (Grand Rapids, Mich. Baker, 1995); Roger E. Olson and Christopher A. Hall, The Trinity (Grand Rapids, Mich.: Eerdmans, 2002); Stanley J. Grenz, Rediscovering the Triune GodL The Trinity in Contemporary Theology (MinneapolisL Fortress, 2004); Brian Edgar, The Holy Trinity in Scripture, History, Theology, and Worship (Oillipsburgm N.J.: P&R, 2004).

And in The Rise of Evangelicalism: The Age of Edwards, Whitefield and the Wesleys Dr. Mark A. Noll tells his readers:

In the context of the eighteenth century, Evangelicals stood with Arians, proto-liberals and anti-confessionalists in championing the Bible against tradition, but they stood with Christian traditionalists in affirming the Bible against reduced views of God, Christ and the Trinity.

As it was with the Bible, so it was also with the other doctrines of classical Christianity. Evangelicalism colored and often invigorated and often invigorated doctrines like the divinity of Christ, the Trinity, the sinfulness of humanity and the human need for divine salvation.

In short, this doctrine is of extreme importance to Protestants and nearly every Protestant Denomination affirms the Trinity, the Nicene Creed, and the Athenasian Creed.

Centrality of the Trinity to Salvation

Acts 16:31 states

They replied, “Believe in the Lord Jesus and you will be saved, you and your household.”

This statement then makes it extremely important what you believe about who Christ said he was. 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 one does not believe that Jesus was a member of the trinity, a part of the triune Godhead, the one does not actually believe in Jesus. 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.

It is for this reason that 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.

Conclusion

Because Protestantism accepts, endorses and upholds Catholic teachings on the issue of the Trinity and Catholicism teaches that belief in the Trinity is required for salvation, Protestant traditions also teach that anyone who denies the Trinity is necessarily unsaved*.

*With a few notable exceptions like Unitarian Universalists and Latter Day Saints