Andrew brought up a point that I often scratch my head about: Why does it matter whether you describe God as the Godhead or the Trinity?
I am not quite sure how my understanding of the Trinity influenced my new understanding of Christ. But given that a greater understanding of the Trinity may have played an important part, I don’t think the LDS should not reject the creeds simply because creedal Christians reject LDS doctrines. I think it is reasonable to accept the LDS view of Godhead as a summation of literal interpretations of the visions of God found in the scriptures, but it is not reasonable to fail to affirm the Trinity as a extremely important explanation that fits in with a larger body of philosophy.
The LDS claim that all we know about God comes from direct experience with God (spiritual experience) and thus we can only really grasp God through spiritual practice, which includes asserting as doctrine the literal meaning of scripture. Joseph Smith’s theology was not in the words themselves, but in the knowledge brought through the Spirit when pondering the words and applying them to life. Joseph Smith describes this position at the tail end of his most important revelation about the three-tiered nature of heaven (D&C 76):
But great and marvelous are the works of the Lord, and the mysteries of his kingdom which he showed unto us, which surpass all understanding in glory, and in might, and in dominion; which he commanded us we should not write while we were yet in the Spirit, and are not lawful for man to utter; Neither is man capable to make them known, for they are only to be seen and understood by the power of the Holy Spirit, which God bestows on those who love him, and purify themselves before him; To whom he grants this privilege of seeing and knowing for themselves; . . .
Doctrines are words attached to mystery. Any LDS who thinks that the scriptures explain God should keep this in mind. God is inexplicable, all knowledge of God is going to be essentially beyond explanation to others. Whatever explanations we do formulate are simply to orient our understanding of God within the other knowledge, perceptions, and beliefs.
The Godhead is a summation of the visions of God. The Trinity does not do this, it is just a philosophical attempt at defining the mystery of why there is only one God that is three persons.
Joseph Smith taught that spiritual visions were more important and carried more authority than philosophical explanations. This may be true, but even so, it would not eliminate the utility of philosophical explanations and catechism for pointing to spiritual truth. It is perfectly reasonable to accept a Trinitarian explanation of God in precisely the same way it is reasonable to accept rights-based interpretation of human government. Likewise, it is fine to conceive of God as a divine Man – as Stephen did in the vision recorded in Acts – because that is how God shows up for some people. What is not reasonable is to take a vision for a reasonable/philosophical/historical explanation, just as it is not reasonable to explain matter by simply re-telling what it looks like.
As I mentioned before, all theology and creeds are existentially the same as the whistling of beavers. The difference between theologies is most simply, the attitude they produce in those who speak and hear them as truth. In some ways, denying the value of the Trinity is similar to denying the value of Newtonian physics. Even if you have proven the validity of the theory of General Relativity, it does not make sense to reject Newton’s theory as vitally useful. Thus, it may be reasonable to posit dogma such as transubstantiation, the Trinity, the hypostatic union, etc. to consistently orient our understanding of scripture with the body of intellectual work that girds our philsophically-minded view of the world — even when these explanations conflict with the literal wording of certain visions.