First, thank you for that very informative essay. I have been a fan of Popper in the sense that I agree with his insight that "subjective experiences of conviction" (from the last quote in the article) can be the only absolute truths. That makes them profoundly personal, which in turn makes them unsuitable as a starting point for justice (unless one were found to be truly universal among human beings). To make any such conviction(s) the starting point of 'just' governance is to start with some people imposing any such 'truth' on all people in the society--and is the starting point for all ideological and theological totalitarian regimes.

If I may, I thought the author of the essay (as well as anyone reading it) might find this interesting: "A New Liberalism" (here in Medium, but not--for the benefit of any 'guest readers'--behind the paywall). It relates how society can be justly governed (which 'old' Liberalism also sought to do) without reference to any 'subjective experiences of conviction', be one secular (which a belief in equality or the existence of a priori Rights, such as "Natural Rights" can be) or sacral. Rather, in it justice follows from the 'falsifiable' observation that human beings have no choice but to effect choices (which I got from Warren J. Samuels). That makes a capacity to choose integral to being human, which makes that a material, universal starting point for an approach to justice.

This approach to justice maximizes liberty, but as a product of justice (not its source, or foundation, or predicate, etc.). 'Equality' is dismissed as an unnecessary complication: all that matters for justice (in this New Liberalism) is that the beings involved are humans. Any Liberal society that came to be governed by this approach to justice would not have to change one bit structurally, but its functioning (its effects on people) would be transformed (most obviously in the economy).