Before there was Sidney, there were the "Schoolmen," the Scholastics, the philosophical descendants of Thomas Aquinas such as the Jesuit priest Francisco Suárez, whose work informed Dutchman Hugo Grotius's seminal work on natural law.
The notion of liberty as a natural right predates the Enlightenment, the Whigs, and modern "rationalism."
SECT. II. The common Notions of Liberty are not from School-Divines, but from Nature.
Tho the Schoolmen were corrupt, they were neither stupid nor unlearned: They could not but see that which all Men saw, nor lay more approv'd Foundations, than, That Man is naturally free; That he cannot justly be depriv'd of that Liberty without cause, and that he dos not resign it, or any part of it, unless it be in consideration of a greater good, which he proposes to himself.
But if he unjustly imputes the Invention of this to School-Divines, he in some measure repairs his Fault in saying, This has bin foster'd by all succeeding Papists for good Divinity: The Divines of the reformed Churches have entertain'd it, and the Common People every where tenderly embrace it.That is to say, all Christian Divines, whether reform'd or unreform'd, do approve it, and the People every where magnify it, as the height of human Felicity. But Filmer and such as are like to him, being neither reform'd nor unreform'd Christians, nor of the People, can have no Title to Christianity; and, in as much as they set themselves against that which is the height of human Felicity, they declare themselves Enemys to all that are concern'd in it, that is, to all Mankind.
—Sidney, Discourses concerning Government, c. 1683
Like any good 17th century English Protestant, Sidney disparages and minimizes the role of Catholicism in creating the emerging political philosophy that would be known as "liberalism," but then again it still goes on today with the 21st century secularists.
Plus ça change.
[See also Timothy Gordon's Plagiarizing Catholicism: Algernon Sidney and the Whigs:
In the end, the only stretch of “intellectual reality” inheres in the American hagiography suggesting that Whig theory was a new American innovation in the late 18th Century…or even a new British one during the prior century…or even a new Northern European Protestant one during the century prior to that.
Whiggism is simply Anglified Catholic political theory imported by sola scriptura Protestants (many of whom were also Enlightenment empiricists) and turned directly against the Catholics in 17th century England—and somewhat less directly against the Catholics in 18th century America. Now how simple is that? Probably not simple enough to plagiarize effectively!]