Thank you for such a thoughtful essay. I see ideologies more specifically as secular religions. Both ideologies and theologies are based on beliefs.
Ideology was invented for the express purpose of replacing religion for justly governing the governance of society. It turns out justice can’t be justly based on beliefs, ideological or theological.
Ideology began with Locke, but he kept God in it. Kant, though he was not an atheist, made Locke’s ideology completely secular, but posited the existence of a transcendental realm of existence that interacts with material reality. That is no different than the Judeo-Christian-Islamic tradition’s beliefs concerning God. Marx was not just secular, but atheistic, but a belief in equality and a belief in a teleological history/present/future for humanity are at the core of his thinking.
I thought you might be interested to consider an approach to justice that involves no beliefs whatsoever: “Real Justice (Summarized for a ‘5 min read’)” here in Medium.