The Renaissance was an age where superstition actually increased. There's a reason most of the art was religious. There's also a reason St. Christopher was a popular image. He's the patron saint that protects against sudden death. People thought they could survive the plague by continually keeping St. Christopher in their sight.
While it's true there's a line ending with Luther that includes Erasmus and other Renaissance thinkers, it also included Christian theological figures going back at least to Gerbert.
The Inquisition was nothing new. Let's not forget about the Albigensian Crusade. I agree about the corruption of the church leading to Luther but the very fact that indulgences were so popular demonstrates that people were very, very religious. I wouldn't conflate the Reformation time period with the Renaissance even if there is an overlap.
But perhaps this should be better reserved for the history forum. My only point is not to overstate the scientific progress of the Renaissance. History rarely, if ever, can be easily divided into ages. The Renaissance was more a period of transition than a sharp reawakening and break from the past.
Yes, I agree, the Renaissance was a period of very slow transition. That time period played a relevant role, towards progression which lead to The Age of Reason. Calling it an interim period of history certainly is understandable IMO. Because like you said, and your perfectly right, many things were going on prior to this reawakening, and after that were not very pretty. These issues with religion and free thought came to a head during the Renaissance (I simply jumble it together with the Reformation, my preference I suppose). To me it was a slow continual, yet absolute fight for progress. Thats why I feel its important.
The reason they try to organize history into ages, is to make teaching it easier. You can relate several points to a certain age to help students remember what they need to know.
As far as CiV goes I feel every age should be touched on. Though I do feel its important to stick to whats mostly relevant, and works well with the games design.