My studies have taught me that morality cannot be anything but subjective. It is always based on belief.
Given your topic, I have something to share that I thought you might find interesting. I have developed an approach to an ethic of justice — an ethic to govern governance in society — that is not based on belief. It does not, however, it get its validity from a claim to ‘objectivity’ (in the sense of a state of mind a person can achieve that is free of extraneous subjective influences); postmodernists, led by Jacques Derrida, have shown that to be impossible for any human being to achieve.
This ethic is, however, materialistic — not in the sense that materialism is the only source of valid knowledge (all beliefs are perfectly valid, for their believers), but because it follows from observation within material existence. It gets its universality (which any ethic must have to be justly applicable to the governance of governance) from the universality of the observations from which it follows. That does seem to take the issue at hand toward the problem of demonstrating a shared intersubjective reality, but this ethic would apply to anyone acting in conformity with those observations, obviating that problem.
If curious, I have Web site, www.ajustsolution.com [Page: real justice] (which the link doesn’t work). I have also published relevant essays here in Medium, such as “From Locke to Real Justice” and, comprehensively, “People for Tolerance, Unite!”