Do any Protestant denominations recognize Latter Day Saints as Christians? Correct me if I'm wrong but I think the Catholic, Anglican, and Orthodox churches do not so that leaves the Protestants.

By Protestant, I mean the 'mainstream' Protestant denominations, with minimal (if any) reference to the more obscure sects. This is because I think the term 'Protestant' belongs to those who accept a handful of certain beliefs (trinity, faith-centered outlook, etc) that are often not present in the more rare denominations.

Do any Protestant denominations (not Latter Day Saints themselves) believe that Mormonism is an acceptable permutation of the "true faith" or whatever the essence of Christianity is or do they only respect their right to self-identify as whatever they want?

I am not interested in potential opinions of individual Protestant believers.
Multiple definitions of Christian

Despite meaning "those who belong to Christ" word Christian is often regarded to mean "Christ-like". On some level, this means that any religious movement or group which seeks to be "like Christ" and claims to follow Christ can make a case for being "Christian".

While mainstream Protestantism often defines "Christian" in this manner, it often uses the word very differently. For example, most denominations will provide adherents and congregants with instructions on how to "become a Christian." This then implies that there are specific criteria which are required to be Christian, and it is not merely being "Christ-like".

Further clouding this issue however is the common belief that in order to be "saved" one must only believe that Christ died for your sins and rose again.

Because this belief is professed by Latter Day Saint (LDS) doctrine, many Protestants often believe that followers of the LDS church are saved.



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 Protestants, and Eastern Orthodox theologians have published numerous studies and books on the Trinity, and they 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 God: The Trinity in Contemporary Theology (MinneapolisL Fortress, 2004); Brian Edgar, The Holy Trinity in Scripture, History, Theology, and Worship (Oillipsburgm N.J.: P&amp;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 Athanasian Creed.



Centrality of the Trinity to Salvation

The reason Protestants often adopt the benchmark of salvation as the determining factor as to the Christianity of an individual or group indicates the fact that there are in fact several criteria for salvation. Let us examine one such criteria.

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, then 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. 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.





Comparing doctrines of the Trinity

This then begs the question, "Do Latter-Day Saints believe in the Trinity?". Upon first glance it may seem so. If you were to ask any LDS missionary this question, they would state yes. They will frequently state that they believe that God is three persons with one purpose. For example,


  Each member of this trinity is called God, and together they constitute the Godhead. As indicated, they are three separate beings, but they are one in purpose, and Jesus repeatedly testified of the unity existing among the three.


During the October 1978 General Conference, First Counselor to the Presidency, Nathon Eldon Tanner stated:


  Each member of this trinity is called God, and together they constitute the Godhead. As indicated, they are three separate beings, but they are one in purpose, and Jesus repeatedly testified of the unity existing among the three.


And according to an FAQ on the LDS web site regarding LDS beliefs,


  
  What do Mormons believe about God ?
  
  
  God is often referred to in The Church of Jesus Christ of Latter-day Saints as our Heavenly Father because He is the Father of all human spirits and they are created in His image (see Genesis 1:27). It is an appropriate term for God who is kind and just, all wise and all powerful. God the Father, His Son, Jesus Christ, and the Holy Ghost constitute the Godhead or Trinity for Mormons. Latter-day Saints believe God is embodied, though His body is perfect and glorified.
  
  
  Do Mormons believe in the Trinity?
  
  
  Mormons most commonly use the term “Godhead” to refer to the Trinity. The first article of faith for the Latter-day Saints reads: “We believe in God, the Eternal Father, and in His Son, Jesus Christ, and in the Holy Ghost.” Latter-day Saints believe God the Father, Jesus Christ and the Holy Ghost are one in will and purpose...


Often the explanation will end there, however in this FAQ, the author continues


  Jesus Christ and the Holy Ghost are one in will and purpose but are not literally the same being or substance, as conceptions of the Holy Trinity commonly imply.


And this distinction is important because the Nicene Creed states:


  We believe in one God, the Father almighty, maker of heaven and earth, of all things visible and invisible. And in one Lord Jesus Christ, the only Son of God, begotten from the Father before all ages, God from God, Light from Light, true God from true God, begotten, not made; of the same essence as the Father. Through him all things were made. For us and for our salvation he came down from heaven; he became incarnate by the Holy Spirit and the virgin Mary, and was made human. He was crucified for us under Pontius Pilate; he suffered and was buried. The third day he rose again, according to the Scriptures. He ascended to heaven and is seated at the right hand of the Father. He will come again with glory to judge the living and the dead. His kingdom will never end. And we believe in the Holy Spirit, the Lord, the giver of life. He proceeds from the Father and the Son, and with the Father and the Son is worshiped...


And the original creed ended:


  But those who say: 'There was a time when he was not;' and 'He was not before he was made;' and 'He was made out of nothing,' or 'He is of another substance' or 'essence,' or 'The Son of God is created,' or 'changeable,' or 'alterable'— they are condemned by the holy catholic and apostolic Church.


The LDS Church however teaches this doctrine arose from the Great Apostasy



Conclusion

Because of this divergence in definition and understanding of the Trinity, Protestants do not believe that Latter-Day Saints are Christian. This is even acknowledged by the Latter Day Saint Church in the March 1988 issue of Ensign magazine in an article titled "Comparing LDS Beliefs with First-Century Christianity" By Daniel C. Peterson and Stephen D. Ricks:


  Since the inception of The Church of Jesus Christ of Latter-day Saints, many critics have denied that it is Christian. Surprisingly, the basis for the claim has little to do with the standard definition of Christian: anyone or any group that believes in Jesus Christ as the Savior and Son of God. Rather, it has to do with Latter-day Saint doctrines that some feel are alien to “traditional Christianity,” where “traditional Christianity” means that body of beliefs held by most present-day Christian churches. The argument essentially goes that if the LDS church believes in certain doctrines not believed in by most present-day Christian churches, then the LDS church cannot be Christian.
  
  ...Latter-day Saints do reject the doctrines of the Trinity as taught by most Christian churches today. For the most part, these creeds—the most famous of which is the Nicene Creed—were canonized in the fourth and fifth centuries A.D. following centuries of debate about the nature of the Godhead.


Similarly in Lesson 136 of the Doctrine and Covenants and Church History Seminary  Teacher Manual, Elder Jeffrey R. Holland of the Quorum of the Twelve Apostles staes


  I think it is accurate to say we believe They are one in every significant and eternal aspect imaginable except believing Them to be three persons combined in one substance, a Trinitarian notion never set forth in the scriptures because it is not true.
  
  Indeed no less a source than the stalwart Harper’s Bible Dictionary records that ‘the formal doctrine of the Trinity as it was defined by the great church councils of the fourth and fifth centuries is not to be found in the [New Testament]’ [Paul F. Achtemeier, ed. (1985), 1099; emphasis added].
  
  So any criticism that The Church of Jesus Christ of Latter-day Saints does not hold the contemporary Christian view of God, Jesus, and the Holy Ghost is not a comment about our commitment to Christ but rather a recognition (accurate, I might add) that our view of the Godhead breaks with post–New Testament Christian history...


So in summary, both Protestant and Latter Day Saint Churches agree that Protestants to not regard Latter-Day Saints to be Christian, the disagreement is merely over whether that assessment is fair and accurate.

Thus the only Protestant groups that would agree would be any denomination which does not profess the Doctrine of the Trinity. To my Knowledge, the only "mainstream" protestant group are Unitarian Universalists.