Religion was only half the reason for the Gregorian calendar reform. Church and state, being interlinked and intertwined, the civil calendar was gradually slipping away from correct calibration with the equinoxes and thus the seasons. So it was important for farmers and mariners and politicians to all have a reliable calendar that matched what the Earth was actually going through.
It just so happened that the religious authority in the West was able to make a significant change to the civil calendar which also happened to match the Church calendar, and it was adopted by all of Christendom, eventually even Asia and the four corners of the Earth have accepted it as universal and not so religious.