From the beginning the Restoration distinguished itself from "orthodox" Christianity in its theology. As Prof. Ronald V. Huggins has pointed out, the theology of the Book of Mormon seems to have been Swedenbourgian expansionistic modalism. See https://mit.irr.org/joseph-smiths-modalism-sabellian-sequentialism-or-swedenborgian-expansionism. You can make your own judgments regarding why that should have been the case, as I have. It does not particularly bother me. Instead, I find it interesting and instructive. In fact, the plain recognition of this strong possibility stands behind the purpose of this entire post, as do other things. Please read on.
It is also reported in the Joseph Smith-History account of the First Vision God's statement to the young Joseph Smith that the creeds of Christianity "were an abomination in his sight." Naturally, this has been a sticking point with fellow Christians who accept these creeds as foundations of the orthodox faith. The Restoration's rejection of these creeds created barriers between Restorationism and orthodox Christianity, which have been eased at times as, for example, when the Reorganized Church (now the Community of Christ) embraced Trinitarianism. This decision strikes me as fairly harmless and understandable, especially in light of the fact that the Community of Christ has always distinguished itself from the LDS Church as shaped by Brigham Young and his unique and criticized (even within the LDS Church) theological views.
That said, one might ask on what historical basis the majority of the Christian community insists on the acceptance of these creeds as a sine qua non of Christian identity. Consider that for nearly three hundred years there were no creeds, and that the first creed came about through the authority and influence of the Roman emperor Constantine. The Nicene Creed of Constantine and subsequent creeds became a major source of confusion and dissension in the larger Christian community, and the theologies of these creeds not infrequently led to schism and bloodshed. Today a little addition to the Nicene Creed in the West, Filioque - indicating that the Spirit proceeds from the Father and the Son - is among the points of contention that separate millions of Catholics from millions of Orthodox Christians.
My focus now turns to Constantine's special contribution to the Nicene Creed, homoousios. Constantine wanted the Nicene Creed to stipulate that the Son, Jesus, is of the "same substance" as the Father. In other words, both of these members of the Trinity possess the same ontological status of divine perfection because they are "consubstantial." No form of the word homoousios is to be found in the books of the Bible, Old Testament or New. It first appears in the teachings of the "heretic" (I don't believe in heretics, but it is important for you to understand how the man is viewed in orthodox Christian eyes) Basilides in the first half of the second century AD. It became a popular term in Gnostic literature, and it was important term in the theology of Sabellius, a modalist of the third century AD who long predated Swedenbourg. Finally, homoousios appears in the Hermetic Poimandres, a text that appears not only in the Corpus Hermeticum but also in the Gnostic Nag Hammadi Library. It was from Hermetism, as Pier Beatrice argues, that Constantine drew his conception of the homoousian nature of the Trinity. See https://www.jstor.org/stable/4146467 .
In Hermetism, the Divine Mind or Nous is the Father and his Son is the Logos. The two are homoousian, i.e., they share the same substance. One wonders whether Philo of Alexandria was aware of these Greco-Egyptian teachings when he presented his theology with its Father and Logos. One also wonders about similar influence on the Gospel of John: "In the Beginning was the Logos, and the Logos was with God, and the Logos was a god." Was Constantine taking Christianity into new pagan territory, or was he only continuing and enshrining a Greco-Egyptian influence that was there from the first century AD? Origen of Alexandria (c. 184 - c. 253 AD) was the first Ante-Nicene father of the Church to teach the homoousian nature of the Father and the Son. Is it coincidental that he was born and educated in Alexandria, Egypt and was also the first Christian father who taught the homoousian view of the Godhead?
Beatrice has argued in favor of the fundamentally Egyptian nature of the theological concept homoousios, tracing it back to five Egyptian oracles of unknown date that were preserved in an anonymous monophysite work of the fifth century AD entitled, Theosophia. In the interest of time, I will only quote one of them:
"There was a unique Nous, more intelligent than all, incorruptible beginning,
from him the intelligent Logos, creator of the universe, eternally incorruptible
Son, reflection of the intelligent Father, one with the Father.
Distinct from the Father only by name,
but one with the Father and one from one, same disposition,
being from the glory of the Father, homoousios, eternally incorruptible
with the prime holy Pneuma (Spirit) and beginning of life."
In the past, these oracles have been seen as "apologetic forgeries fabricated with the aim of artificially demonstrating the harmony between pagan wisdom and the Christian revelation" (Beatrice, p. 262). However, nothing about these oracles is inconsistent with Greco-Egyptian teachings of the Roman era. Thus it appears that the roots of Christian Trinitarian theology are to be found in the Greco-Egyptian religio-philosophical thought of Roman Egypt.
I write this not to challenge the legitimacy of these ideas but 1) to provide their proper historical background and 2) now to show what this could mean for Restoration theology. Notice how the Egyptian oracle cited above, which was allegedly inscribed in the subterranean passages of the Valley of the Kings near Thebes in Upper Egypt, resonates with Joseph Smith's teaching regarding "intelligences" in the Book of Abraham, as now found in the LDS Pearl of Great Price. There God says to Abraham that he is "more intelligent than they all" (Abr. 3.19), or, in other words, greater than all of the other intelligences. This would make him the equivalent of the Egyptian oracle's Nous.
There is, however, a crucial difference between the Egyptian theological oracles and Joseph Smith's teachings in Abraham 3. The Egyptian oracles refer to the Nous, Logos, and Pneuma, or the Father, Son, and Spirit, and speak of them being homoousios and most intelligent, but they say nothing of humankind's relationship with these entities. This omission, however, does not mean that all Greco-Egyptian thinkers were silent on this subject. Plotinus (c. 204 - 270 AD), the most important figure of late antique Platonism, taught that the highest aspect of the human being was its undescended soul, residing with the Nous, that was homoousios with the One. In other words, there is an aspect of the human soul that is identical in its substance with the One or, one might say, God. The goal of the individual was to achieve henosis, which was an ascent to unity with the One, which started with a realization of the one's own highest homoousian aspect.
I am not claiming that Plotinus was a proto-Restorationist or that Joseph Smith must have read Theosophia or Plotinus. Rather, I am trying to show that the very same font that eventually provided the intellectual framework for constructing Trinitarian theology has the resources for constructing a Restoration theology that encompasses Restoration teachings from the First Vision all the way to Nauvoo and perhaps might even untangle the mess that became Brigham Young's Adam-God doctrine. Past generations of Restorationists have eschewed "the philosophies of men" in the hope of finding a purer Christian doctrine. What was not understood was that Christian doctrine was always already a synthesis of different cultural strains including Jewish, Persian, Egyptian, and Greek ideas and sources. Now that archaeology and other scholarly disciplines are revealing more precisely these relationships, Restoration thinkers and writers can use them more productively to the advantage of rendering its ideas intelligible as early Christian fathers once did for Christianity.
Before I end, I must bring everyone's attention to the work of Dr. Stephen Fleming, whose 2014 dissertation ("The Fulness of the Gospel: Christian Platonism and the Origins of Mormonism") traces the Platonic Christian threads that informed Joseph Smith's views and doctrines. Fleming acknowledges that Smith did not identify himself as a Christian Platonist, but he argues persuasively that "[Joseph] gravitated towards such ideas, which were available to him through a variety of routes, including popular forms of religiosity embraced by his family; the views of key followers; and the scholarship of his day as summarized in histories, encyclopedias, and other reference works." As the Restoration matures, work such as Fleming's will help Restorationists articulate the doctrines of the Restoration more clearly and robustly, placing it on par with other theological systems and making it more compelling to those who have been spiritually converted.