Galileo and the Catholic Church: who was right?

This time we are talking about a book by Galileo Galilei, the Dialogue about the Chief World Systems, which was put into the Index of Forbidden Books in Protected content removed from it in Protected content . We are also talking about an article by the philosopher of science Paul Feyerabend, who thought that the Church was right because the fragmented, specialistic modern science initiated by Galileo was not conducive to a good and just society. But things are complicated - the late Pope John Paul II disagreed with Feyerabend. So, what is the effect of science on society? Does science undermine society's foundations?