Read the literature: the writings of the philosophes and the English, Scots and German enlightenments, the historical work of period (think Gibbon and Hume), the writings of the Founders, Burke, and the vast secondary literature on the questions that has grown up over the past 250 years. It is impossible to have a discussion when we don't even agree on the basic facts.
It is amusing that you use Burke as an example. Burke regarded ordered liberty, not confusing license with liberty, as central, which is the central point of John Paul’s statement. This view of ordered liberty provided the basis of his support of the American Revolution and his rejection of the French Revolution. Burke was a Christian and viewed religion as fundamental to civilization.
“Nothing is more certain, thus that our manners, our civilization, and all the good things which are connected with manners and civilization, have depended upon two principles, the spirit of a gentlemen, and the spirit of religion.”
Burke
“Freedom, and not servitude is the cure of anarchy; as religion, and not atheism, is the true remedy for superstition.”
Burke
“What is Jacobism?” “It is an attempt...to irradicate prejudice out at the minds of men...Jacobins have resolved to destroy the whale frame and fabric of the societies of the world, and to regenerate them after their fashion. To obtain an army for this purpose. they everywhere engage the poor by holding out to them as a bribe the spoils of the rich. A Christian, as such, is to them an enemy.”
Etc.
Newton has been called the “starburst of the enlightenment.” He was a devout Christian, to the point of lifelong celibacy, and spent the bulk of his time studying the Bible. He owned copies of scripture in the original Greek as well as Latin and wrote entire treatises on books within the Bible.
Gibbon is Gibbon. He was anti-Christian, anti-Jewish, anti-monotheistic religion; however, his view was outside the norm as shown by contemporary reaction and attack against him on this very basis.