If you look closely at the historical record, many of America's Founders speak positively of something known as "Primitive Christianity." I won't provide the quotations (just yet). You can either trust me or look it up yourself.
But what does that term mean? American Creation's Tom Van Dyke might answer Christianity "adulterated by man, i.e., the papists...." There certainly is a strong kernel of truth there, but also a larger picture as I explain below.
I've observed when certain figures -- some of America's Founders and their influences over whose proper religious categorization we argue -- refer positively to something known as "primitive Christianity," they mean they believe Christianity was corrupted by the "church" early on.
Now that's something in which a good evangelical or reformed Protestant can believe? Corruption in the church necessitated the Reformation. Well, not exactly as I will explain below. Back then "primitive Christianity" was very often (though perhaps not always) a code word for Christian-Deism, Christian-Unitarianism, and today is something a Mormon or Jehovah's Witness would feel comfortable with.
You see, for many, perhaps most of these folks who valued "primitive Christianity," the Church at Nicea was already corrupted. And indeed, these folks think of the Nicene Church as a "Papist" one (and therefore illegitimate). The problem is Anglicans, capital O Orthodox Christians and most reformed and evangelical Protestants wish to claim and feel in communion with the Church at Nicea and the Nicene Creed.
Folks like certain Baptists who believe both in the Trinity but think the Nicene Church was already Roman Catholic are the oddball outliers among Protestant Trintarians. (See the fourth paragraph in this piece written by American Creation's Brian Tubbs, himself a Baptist pastor, on why Baptists might have such disproportionate oddball theology.) The Quakers who believe in the Trinity, but not creeds, likewise qualify as Trinitarians who might endorse the notion that the Nicene Church was corrupt and "real Christianity" was the "primitive" one of the ante-Nicene era.
But it's mainly those who reject the Trinity that are interested in attacking the Council of Nicea. Indeed, notable unitarians blame the doctrine of the Trinity on the "Papism" of Nicea. For instance, John Adams:
"The Trinity was carried in a general council by one vote against a quaternity; the Virgin Mary lost an equality with the Father, Son, and Spirit only by a single suffrage."
-- To Benjamin Rush, June 12, 1812.
And since the Church around the time of Nicea was the one who selected and finalized the books of the canon (i.e., "the Bible") some of the professors of "primitive Christianity" disregard entire books of "the Bible" and blame it on "Papism," i.e. the Church who wrote the Nicene Creed. (And not just "books" of the Catholic Bible, but of the Protestant Bible as well like the Revelation of St. John.)
It was this same mindset that led Christian-Deists and Unitarians like John Adams to both 1. reject the Trinity, and 2. think "the Bible" was an errant, corrupted book, that nonetheless contained "the Word of God" underneath the error and corruption.
In today's day and age, folks who believe in sacred scripture as the "Word of God," but not the Trinity (i.e., the Mormons and Jehovah's Witnesses) are ones likely to 1. have an affinity for the "primitive Christianity" of the ante-Nicene era and 2. seek to "restore" the faith to what it was before it got corrupted.