That is a very useful distinction. It is important to recognize both as forms of knowledge.

Another way to put the distinction is 'immaterial' and 'material'. The latter is knowledge pertaining to material existence. The former refers to intuition, 'feeling', beliefs, etc. Beliefs can be secular/ideological or sacral/theological.

The problem described in the article at hand is the problem of how governance should be governed: how to determine how individuals should treat one another and how a society's political process and its economy should be structured--as well as determining their sanctioned functioning. Those are matters of material existence: human life as experienced in the 'real world'. Only material knowledge can produce an adequate solution for that problem.

All immaterial knowledge is inherently non-rational. We can reason about such knowledge and reason from it, using such knowledge as a starting point, but accepting it as knowledge is ultimately a non-rational thing: we can reason our way close to acceptance of such knowledge, but we cannot reason our way all the way to accepting any such knowledge. All immaterial knowledge requires at some point a Kierkegaardian "leap of faith."

That makes all such knowledge entirely personal and, from the point of view of any other person, completely arbitrary. That makes any such knowledge invalid for justly governing governance.

To my mind, the only thing gotten completely right by John Locke (the godfather of the meta-ideology of Liberalism, Two Treatises of Government: 1689) was his conclusion that injustice is arbitrariness in human relations. If the governance of governance is itself arbitrary--as it must be if based on any immaterial knowledge--then, to paraphrase words attributed to Jesus, 'how great is the injustice'!

If curious, a completely material approach to how governance should be governed is at "Can't Get Any Simpler" (a "2 min read" here in Medium with links to more about it--with nothing I publish here behind the paywall).