Linear thinking is both standard Western thinking and also "Half Thinking" since only half of our brain is linear and the other half holistic. For the anchor question the answer is "there is no anchor" since it's like asking for the anchor block on a pyramid in Egypt or the anchor to technology.
Ergo, not only do I disagree with Tocqueville's assertion that there is an anchor point, but also his Eurocentric view of Catholicism.
If we want to draw points along the line of mankind's move toward democracy, we can, indeed, look at religions and rich aristocrats because they were the only people who 1) knew how to read and 2) had the time to play chess, read books and contemplate the mysteries of the Universe. Everyone else was dying of bubonic plague and working in the fields.
John Locke, a Protestant hehe, was one of the greatest minds to influence modern democracy: https://en.wikipedia.org/wiki/John_Locke
No doubt Locke and Montesquieu played outsized roles in the minds of the framers of the constitution.
I do not think Christianity directly created democracy, and I think Tocqueville is on the wrong track claiming catholicism is more amenable to democratic traditions than protestantism.
But I think he had a legitimate insight that Christianity - Protestantism in particular, IMO - was fertile ground for the germination of democratic traditions. Largely because Protestant Christianity preached spiritual equality, it eschewed heirarchy and traditional authority, and it embraced individualism and mercantile capitalism in a way that Eastern Christianity, Islam, Hinduism, Confucianism, et al. did not.