I'm going to say this before I check out Emperor Constantine's timeline, but I think one interesting possibility is that the German Peasants War may have gone differently. On one hand, the uprising was provoked by the nobility tightening the screws on the peasantry in terms of rents, feudal rights and the legal system more than it was the Reformation, so it would still happen. On the other, Martin Luther's ultimate condemnation may have had a crucial role in curbing it and preventing it from co-opting the Reformation. So one interesting (albeit unlikely, the military dimensions of this being what they are) possibility would be a longer, stronger, more durable rebellion.
Where that might get really interesting is that I think there's a tendency to idealize Muentzer and his colleagues. The societies they might create might be far from appealing.
Once again, all this is somewhat unlikely, but nonetheless this is where the prompt sent my thinking.