and shook Europe's faith in God.
If something, that's definitely the contrary; you had a really important and deep wave of christianisation of social and political life, really deeply rooted : christianisation of names, toponyms, revival of relic cult, etc.
It could have been delayed, but it would have happened sooner than later, eventually. It was just at the doors and a return of the plague (BD bacilla seems to have been the same than Justinian Plague's) was likely.
And if there is no Black Death, would the Renaissance have occurred on schedule, later or not at all?
For starters, it would have provoked a substituance crisis : too many people with the agricultural production not able to stick on needs. You already had important starvation crisis in the early XIVth century.
One should remember that the emancipation process was already on the rails in Western Europe : serfdom had largely disappeared there before the plague hit.
You'd have social changes : a lesser urbanisation (many people going to refugee themselves on cities), but as well a less opportune situation for popular classes (not only what would remain of servage, but as well free peasants and denizens).
Culturally, the whole pious and "medieval" Great Awakening movement (use of bilbical names being far more widespread being a clue) would be butterflied and it would have a great impact : lesser persecution of Jewish communauties, no art works on macabre or at the contrary "fleeing" in pleasure genres.
I'd think that if a Renaissance-equivalent appears (as it's likely at this point) it could be more in the general continuity than IOTL ( "
XIIth's Renaissance",
Pre-Renaissance and Trecento, etc. with still a distinct spirit for a "XVth's Renaissance" : classical Antiquity was knowing a revival since some time) rather than opposed to a Late Middle Age seen by its proponents as ridden by epidemics, mysticism and cynism (basically the main point of IOTL Renaissance was less it was a thing, than that it was concieved as a radical rupture with the immediate past).