The key event in the Renaissance that began the decline of religion was the Protestant Reformation. It is not that the Protestants were not pious. Members of the movement were devout reformers who believed that Roman Catholicism had become corrupted by the great wealth and power of the Church, and wanted to return to what they saw as the roots of Christianity. However, one effect of the Reformation was breaking the stranglehold of the Roman Catholic Church on power and the beginning of the principle of freedom of religion. While once, one needed to be a member of a Church, at least nominally (whatever one actually believed in one's heart and mind) in order to have a career, attend university, or even be able to live without fear of being deprived of one's property or even life, religious choice meant that people who are by nature atheists or skeptics are not compelled to be nominal members of a church for practical reasons.
The next major contribution of the Renaissance to the decline of religion in Europe was the rise of critical philology, which began to reveal ways in which the Bible was not perfect, including apparent contradictions and grammatical errors. This undermined the notion of plenary verbal inspiration. Also, the sola scriptura doctrine of the Protestants, emphasized critical individual reading of the Bible as all that was necessary for salvation, thereby undermining the Church and organized religion.
Finally, the Renaissance was a period of recovery of classical texts and exploration, making people aware of the varieties of different religions in a way that tended to undermine the truth claims of each individual religion.