Primitive Christianity appeals to among others Quakers, Unitarians, Christian-Deists, and more. Like all of the variants of "Christianity," it sees itself as the one authentically representing the teachings of Jesus and his followers. However it believes that by the time the Nicene Creed was written the faith had already been corrupted. It blames the Nicene Creed on Roman Catholicism.
The Catholic Church of course, would gladly take credit for the Nicene Creed. But the vast majority of "orthodox" Protestantism believes in that creed, feels in communion with the church who wrote it, and no, does not believe Catholics should be credited for it.
Primitive Christianity is radically individualistic, anti-creedal, and anti-clerical. It's not necessarily theologically unitarian, but the method obviously lends support to such. Trenchard and Gordon define and defend the concept of Primitive Christianity in great length here. We see, among other things, the Roman Catholic Church is the chief villain. High Church Anglicanism isn't much better. And the entire clerical class of all Christian churches is tarred.
Here is a passage where they claim to be agnostic on the Trinity, and declare the question to be irrelevant to the expression of the faith:
Since ’tis agreed amongst all our present Sects of Christians, that the Saviour of the World is the Son of God, descended from Heaven to teach Virtue and Goodness to Men, and to die for our Redemption; how are we concerned in the Scholastic Notions of the Trinity? Will the Scripture be more regarded, or the Precepts of it be better observed, if the Three Persons are believed to be Three Divine distinct Spirits and Minds, who are so many real subsisting Persons? Whether the Son and Holy-Ghost are Omnipotent of themselves, or are subordinate, and dependent on the Father? Or, if they are independent, whether their Union consist in a mutual Consciousness of one another’s Thoughts and Designs, or in any thing else? Whether they are Three Attributes  of God, viz. Goodness, Wisdom and Power? Or Three internal Acts, viz. Creation, Redemption and Sanctification? Or Two internal Acts of the One subsisting Person of the Father; that is to say, the Father understanding and willing himself and his own Perfections? Or Three internal Relations, namely, the Divine Substance and Godhead confidered as Unbegotten, Begotten, and Proceeding? Or Three Names of God ascribed to him in Holy Scripture, as he is Father of all Things, as he did inhabit in an extraordinary Manner in the Man Jesus Christ, and as he effected every thing by his Spirit, or his Energy and Power? Or lastly, Whether the Three Persons are only Three Beings, but what sort of Beings we neither know, nor ought to pretend to know? which I take to be the Trinity of the Mob, as well as of some other wiser Heads.And here they are on the Quakers and why their example demonstrates that Great Britain didn't need an established Church:
Now it seems to me, that the Toleration or Liberty of Conscience granted by Law in England, gives us an Opportunity of examining this Matter, beyond what can be done in Popish or other Countries, where no such Toleration is allowed. We have a numerous Sect, or People among us, distinguished by the Name of Quakers, who have no Spiritual Officers, with any Wages, Hire, or Salary, whose peculiar Business it is to Teach; but every Man among them does freely of himself, and gratis, communicate his Knowledge, both publicly and privately, according to his Ability, whenever he judges it proper so to do: And therefore we may easily make a Comparison in the Case, between the Wisdom and Virtue of the common People of the National Church, and the Wisdom and Virtue of the Quakers, (who have no Quality or Gentry among them; but consist of Tradesmen, Artificers, Farmers, Servants, and Labourers) and thereby make a  just Judgment, whether the Two Millions per Annum are well or ill bestowed.They make an interesting argument which you can read for yourself: Because the Quakers all read the Bible for themselves as opposed to relying on the Priestcraft to read, interpret and spoon-feed it to them (and what they are getting spoon-fed distorts the Bible), the Quakers not only end up understanding the Bible better but have their literacy rates improved over that of the vast majority of ordinary folks sitting in the pews of the Church of England.