To a degree, but there was still a lot of fighting and killing over religion in Europe. The whole UK Catholic vs Protestant thing for instance.
But the Catholic vs Protestant split occurred precisely because the newly-formed northern European nation-states wanted to absorb religion into the state apparatus. The Catholic Church, after all, was a foreign power centre which often tried to exert control over the nation-state; for example, by excommunicating a ruler or even an entire nation (e.g., England under King John). The monarchs of northern Europe weren't having this; they wanted a compliant and loyal Church which would obey their orders. In other words, a
national Church....
If you're talking to an american then from our point of view most of Europe doesn't really have full separation of church and state today. You have state churches and stuff like that.
The national state religions of Protestant Europe were an attempt to
reverse the division between Church and State which had hitherto existed in Christendom. But, unlike the case with Islam, the state would absorb religion into itself rather than religion absorbing the state into itself.
The catholic church was perhaps the most powerful organization in the medieval world was it not?
Indeed it was. But that was not to last....
"Politics is the art of looking for trouble, finding it everywhere, diagnosing it incorrectly and applying the wrong remedies." - Marx (Groucho)