Why were the authors of the U.S. Constitution opposed to the establishment of a national religion?

Because the founders wanted to construct a nation of freedom, based on Locke's principals in the pursuit of life, liberty and property (which they changed to happiness). In making this new nation religiously free, it allowed people to practice their own religions without discrimination. It was an aspect of democratic ideals, but probably also in the fear that religious wars such as those that occurred in the past couple centuries in Europe may erupt in America, such as the 30 Year's War, with bloody violence over the dominance of Catholics and Protestants.