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.
The extent and nature of Burke's Christianity is, to say the least, obscure. Burke distrusted 'speculation' and said (in the Tract on the Popery Laws that "For the Proestant religion, nor (I speak it with reverence, I am sure) the truth of our common Christianity, is not so clear as this proposition - that all men, at least a majority of men in the society, ought to enjoy the common advantages of it. Lord Acton, the famous 19th century historian, thought this meant Burke was insincere in matters of religion, though some other scholars disagree. Burke also wrote in the 1750's, in A Notebook of Edmund Burke Metaphysical or Physical Speculations neither are or ought to be, the Grounds of our Duties; because we can arrive at no certainty in them. That is to say, the truth of our common Christianity is essentially a matter of faith and not of reason. Burke, deeply concerned with the organic development of institutions, (in the felicitous phrasing of the philosopher Burleigh Wilkins in his The Problem of Burke's Political Philosophy) occupies a middle position, distrustful of the rational pretences of the deists, on the one hand, and the emotional enthusiasm of the Methodists on the other
And, of course, Burke is not really a classical liberal precisely because of his traditionalism. He is in many respects sympathetic to the elements of classical liberalism that evolved organically in England up through the 18th century, including the very 'rights of Englishmen' he defended in the colonists, and a useful and early opponent of the reductio on classical liberalism which the French Revolution became.
This stuff is much more complicated than you would like it to be.