But I question the assertion that "all so-called facts are in the end merely beliefs".

Are you really disputing the concept of objective reality?

These are two different things. Objective reality is what it is; "facts" are propositions we make in assessment of objective reality: thoughts and impressions of what reality actually is. Many people conflate "fact" the assessment of objective reality with "fact" as objective reality itself. In many practical applications, this distinction isn't particularly relevant; but philosophically it is fundamental. It has to do with the subject-object dichotomy, and the fact that reason cannot traverse it (because reason is based on it).

As an example, "trans women are women" is an opinion, not a scientifically verifiable fact. It could become the majority opinion in some countries and not others, but it will never be an objective fact

These two things are separate and distinct. How do you know "trans women are women" isn't already "objective fact"?

Appreciating the distinction between objective reality and our subjective impressions about it can clear many things up for you and provide you with some startling insights.