At the time, the catholic church had a reign of terror. Going against religion was considered heresy and sometimes punished by death so it's not a surprise everyone were claiming to be good Christians and doing everything to look like good Christians. However, the Italian renaissance ideals were definitely moving away from Christian dogma and towards a more mechanistic, scientific, humanistic and secular interpretation of the universe.

I find Michaelangelo's sistine chapel representation of god being in the shape of a human brain a good example of the whole situation. They were trying to convey subtle messages so that the pope wouldn't notice. Given that Michaelangelo and Leonardo were pioneers on human dissections, IMO it is unlikely a coincidence. http://www.byui.edu/onlinelearning/courses/hum/202/CreationOfAdamBrain.htm