I think the Acton Institute does a credible job arguing a good scholarly case that religion or Christianity is necessary for human rights.
I think though, that, based on what the Bible says in its text and the history of the Christian West, groups like the Acton Institute will at best have a half-full argument. The other side will always have a half-empty critique. It's a "selective" reading of both the Bible and the history of the Christian West that supports notions of God given human rights, liberty and equality. And the most notable expositors of unalienable human rights were men like Thomas Jefferson who, though they believed in a rights granting God rejected every single tenet of orthodox Christianity as Jefferson did in his October 31, 1819 letter to William Short, where he listed by name and rejected the following:
The immaculate conception of Jesus, his deification, the creation of the world by him, his miraculous powers, his resurrection and visible ascension, his corporeal presence in the Eucharist, the Trinity; original sin, atonement, regeneration, election, orders of Hierarchy, &c.
So whatever belief in unalienable rights depends upon, it does not depend upon believing in those things; it is not by virtue of belief in those things that our notions of unalienable human rights derive.
In one of my favorite posts of his, Larry Arnhart explains the "half-empty" critique that skeptics will always be able to raise against traditional Christians who try to argue that the Bible and the orthodox Christian religion are where notions of human rights derive and must rest:
The case of slavery and "universalism" illustrates the problem....[M]any religious traditions have allowed slavery, and the Bible never condemns slavery or calls for its abolition. On the contrary, in the American debate over slavery, Christian defenders of slavery were able to cite specific biblical passages in both the Old Testament and the New Testament supporting slavery. Opponents of slavery had to argue that general doctrines such as the creation of human beings in God's image implicitly denied the justice of slavery. But they could never cite any specific passage of the Bible for their position. Here's a clear case of where the moral teaching of the Bible depends on our coming to it with a prior moral understanding that we then read into the Bible.
Moreover, the "universalism" of the Bible is in doubt. I don't see a universal morality in the Old Testament. Moses ordering the slaughter of the innocent Mideanite women and children, for example, manifests a xenophobia that runs through much of the Old Testament.
Now, of course, the New Testament does seem more inclined to a universal humanitarianism. But the Book of Revelation teaches that at the end of history the saints will destroy the Antichrist and the unbelievers in bloody battle. The bloodiness of this vision has been dramatized throughout the history of Christianity. (See, for example, Tim LaHaye's popular LEFT BEHIND novels.)
....And, of course, there is a continuing controversy over whether the Christian churches in Europe did enough to oppose Hitler. The German Lutheran Church was inclined to interpret the 13th Chapter of Romans as dictating obedience to the authorities. Martin Luther himself was brutal in his expression of anti-Semitism. How would Holloway explain cases like this? Would he say that the true doctrines of biblical religion always require universal love, and therefore any behavior by a biblical believer that violates universal love is based on a misinterpretation of biblical doctrine?