I agree wholeheartedly with your analysis concerning beliefs. I think one trap people fall into is equating secularity with objectivity.

There are such things as secular beliefs, which can be no more ‘rational’ than any religious belief can be. Two examples of secular beliefs are believing in human equality and believing in the existence of a priori Rights, such as a Right to liberty.

Unfortunately, those beliefs (which many people also claim to find in the Bible) underlie Liberalism. That means that Liberal justice, based on equality and liberty, can only exist as an arbitrary privileging of those particular beliefs over any others (such as believing that men are inherently superior to women, or that this race is inherently superior to that one).

“Real justice” is a strictly rational approach to justice. Its ethic follows from observations within material existence, not belief, whether religious (theological) or secular (ideological). That ethic can therefore (potentially) be ‘falsified’ (in the scientific meaning of that term).

That means that if that ethic cannot be falsified, it must be accepted as valid until such time as it might be. That might be never: there are truths verified by observation within material existence that are as valid today as they were the day Adam first gazed on Creation, such as the existence of ‘gravity’. (Although our understanding of it has evolved, and is not yet complete, gravity itself is whatever is always was.)

Applying the ethic of real justice (mutual respect in effecting choices) to the governance of society would maximize liberty as a practical matter, reinforce political democracy, and transform the social and environmental outcomes of the existing economy.

A brief (”5 min read”) summary of real justice is here in Medium.