The main impact of this sort was that the Scientific Revolution led to challenges to the authority of religious leaders.
This sort of challenge can be seen most clearly in cases like that of Galileo. Galileo was famous for, among many other things, coming into conflict with the Catholic Church. The Church at that time held that the Bible proved that the Earth was the center of the universe. This belief was held on the basis of religious authority. But Galileo believed that he had disproven that idea through the scientific method. He defied Church leaders on the issue and was punished for it.
In ways like these, the Scientific Revolution led to a questioning of authority. It led to the idea that things needed to be proven scientifically rather than simply taken on faith because the Church (or some authority like Aristotle) asserted that they were true.