I don't seriously disagree with anything in this article. I do want to point out, though, how that (full) quote relates to all ideologies, including the ideology of Liberalism.
Reason and rationality are not the same thing. Sound reasoning is the implementation of sound logic in argumentation. People can reason perfectly well from beliefs. Beliefs are non-rational. That makes any chain of reasoning from beliefs non-rational.
A great example is Paul in the Bible. He was a brilliant logician, but it all followed from his beliefs about God, Jesus, and his own spiritual experiences. That doesn't make him wrong or unreasonable, but it does make his output non-rational. (The late Ravi Zacharias is a more recent, very excellent example of the same process.)
All ideologies are based on beliefs as surely as Paul's theology was. Marx was, I argue, a radical equalitarian, not a materialist. He projected his beliefs onto a dialectical interpretation of history that made the ends he desired for society a historical inevitability, not merely the expression of his personal beliefs. Liberalism is based on believing in equality and the existence of a priori Rights, including a Right to liberty. Fascism in all its iterations is based on a belief in the inherent superiority intrinsic to some group of people (of which the adherent always just happens to be a member). Again, arguments that are logical as all get-out can be constructed in support of any of those ideologies, but all remain equally non-rational--and "lived reality" in any society governed on the basis of any of them non-rational if not irrational.