Our history isn’t as lacking as popular imagination thinks; the short answer to your question is “very”.

The long answer is delved into by Chris Wickham in The Inheritance of Rome: A History of Europe from 400 to 1000, from around chapter 3 onwards. Wickham notes early on the changing demographics:

Christians were for the most part numerically dominant as well. But we must ask what sort of Christianity this was, what effective content it had: how much it absorbed traditional Roman values (and even religious practices), how far it changed them, and what its own fault-lines were, for there were many of these.

And then goes on to explain that the conflicts over, eg the nature of Christ and how bishops were consecrated got very serious indeed:

So heresy was both increasingly dangerous and increasingly common in the late empire. It was regarded as a problem in later centuries, too (particularly in the thirteenth-century West), but only the Reformation matches the intensity of the religious disputes of the period 300–600.

That last bit drives home the short answer; the Reformation period saw the European wars of religion, and, drawing on contemporary histories and records, Wickham shows that the disputes of 300-600 were indeed as intense, often requiring intervention by the Emperor. These disputes spawned Arianism and Nestorian Christianity and the split between Chalcedonian Christianity and Monophysitism and so on; the oldest schisms in the Christian faith - some of which endure to this day - date to this period.

I’m really not doing it justice I admit; you can purchase The Inheritance of Rome from Amazon here. I do recommend it as Wickham has shown his work on the subject.