Is it a coincidence that the nations which industrialised first were Christian?

Some good answers here, but none giving the obvious reference: Jared Diamond, Guns Germs and Steel. It was despite (mediaeval) Christianity: Byzantium stopped all science very early. The Islamic world was into Science before Christendom was, and the switches in both worlds were not about the religion, but about interpretations of the religion.

As for why Christianity went big time when it hit Europe: that’s all about the Roman Empire and its successor states, and the power vacuum to its North. And about the Persian Empire rejecting Christianity as a Roman thing.