This is a claim that commonly appears online in discussions around Christian Universalism (the belief that everyone will ultimately be 'saved' in a Christian sense - 'everyone goes to Heaven eventually', if you will), and as far as I can tell the specific formulation originates with Edward Beecher in the 19th century. But how accurate is this description of Christianity a couple of centuries after the Resurrection? Can we really identify several distinctive 'schools' of theological belief in the early Church, and if so, what are some of the key things that distinguished them from each other and what are the geographical or social contours of this state of affairs?
Just to be clear, I am a Christian who believes in universal salvation myself, and I'm not necessarily asking about the claim as it specifically relates to the history of that belief - this is just the context I've encountered it in. It's the kind of 'fault lines' in early Christianity in general that intrigue me here, and especially the idea that there were (according to this claim) already half a dozen fairly distinct, cohesive schools of thought so early in the Church's history.
It's poorly conceived and not representative of modern understandings of 3-5th century theology.
I presume you mean something like the characterisation presented here in Beecher's History of the Doctrine of Retribution?
The major issue, I'd say, with this characterisation, is that it over-emphasises the very idea of 'distinct' schools located in geographic centers and having very distinct theological ideas as a 'bloc'. Yes, there certainly is a, for example, "Alexandrian" tradition. But our knowledge of that tradition primarily comes from looking at every theologian that is associated with Alexandria and attempting to "lowest common denominator" them.
A good example of how this idea of 'schools' is open to severe critique, is the long standing idea that there were two main schools of exegesis - Alexandria vs. Antioch. Fairbairn dismantles this notion in a 2007 article, pointing out (in part) that it assumes a uniformity among the supposed adherents/representatives of these schools that simply isn't there.
Patristic scholars these days are far more likely to talk about 'trajectories', 'influences', and individual theologians and their thoughts, than monolithic 'schools' per se. Certainly not of the mass-bloc type that Beecher is writing about.
Of course, there are different types of fault lines across the early church - geographical, linguistic, theological, but these do not always line up as neatly as "Alexandrians taught X, Caesareans taught Y."