Oh, it's so awful, the way that laypeople talk about early Christianity without having either A) a clue or B) any trust of those who do have a clue because they study such things all day every day for a living, the theologians and Biblical scholars, and C), the way that the experts unfortunately often enough give the laypeople reason to distrust them -- it's all such a mess.
One example out of -- thousands, probably, is the way that the widespread error persists that the Bible was re-written or at least edited at the Council of Nicea in AD 325, a notion for which there is not a shred of historical evidence -- and there are quite a number of contemporary and near-contemporary descriptions of the Council.
It seems that two different things are being confused here:
1) The purging of the Arians. I don't dispute that this got underway on a large scale at the Council of Nicea. I certainly wouldn't call Constantine an innocent bystander in this process, although I speculate -- speculate! -- that if the Arians had formed a majority at Nicea, Constantine might've sided with them and begun the purging of their opponents, because his primary concern was that the Christians stop fighting among themselves and agree to some degree about what their religion was and what it stood for. He cared about political order, not theology.
2) A 4th-century rewrite of the NT. I do dispute that this took place. Some Gnostic texts were destroyed along with the wiping out of the Arians, but these all dated later than the texts which were later canonized, and the texts which were eventually canonized were all or almost all already accepted by most Christians well before Nicea. Irenaeus, for example, (ca130-ca200) refers to the four eventually canonized Gospels at around the time that the Gnostic Gospels were first being written. He quotes from 24 of the present 27 NT books, all but Hebrews, III John and Jude.
Hopefully it's clear that I don't have a theological stake in any of this. I don't believe in God, I'm not sure whether Jesus existed, I don't believe in walking on water or rising from the dead or other miracles. I don't believe in any Christian doctrine, canonical or heretical, nor do I have any non-Christian religious (or spiritual or mystic, po-TAY-to, po-TAH-to) beliefs. I'm interested historical accuracy here. That's all. And when it comes to the Council of Nicea and the Bible, the historical record is unusually clear.