I had tried to avoid engaging in grand metaphysical “ism” talk, but it seems that resistance is futile! So here are brief thoughts, in the context of theorising gender.
We can safely assume that there is a reality to people’s gender-relevant experiences and biochemistry which exists independently of our understandings. Taking this (to me obvious) stance is known as ontological realism. Theorising, about gender or otherwise, is done by people who have imperfect and indirect access to reality and theories evolve over time. Our vantage point—beliefs, biases, values, experience, privilege and oppression—has an impact on our theories, so two gender theorists doing the best they can with the available evidence can produce very different explanations (epistemic relativism). This is true of any science where multiple theories are consistent with evidence; in other words, the theories are underdetermined by evidence. It is also true when we theorise about ourselves and try to work out our own gender.
Even with this relativist mess, manifesting as bickering in scientific journals and conferences, consensus can arise and one theory can be declared better than another (judgemental rationality). However, there are often many different ways to classify biological, social, and other phenomena, even with impossibly perfect access to reality (this has a great name: promiscuous realism).
The underdetermination of theories means that something beyond evidence is needed to decide how and what to theorise. Scholars in the critical theory tradition are required to pick a side in a social movement, for instance feminism, anti-racism, trans rights, or an intersectional composition thereof. It is not enough for a critical theory to be empirically adequate; it also has to help chosen social struggles make progress towards achieving their aims. Two theories may be empirically indistinguishable but one transphobic; from a trans rights perspective, the transphobic theory should be discarded.
(For more on epistemic relativity, ontological realism, and judgemental rationality, see Archer et al. (2016).)
Now we can make sense of what it means to be assigned female or male at birth. What is assigned is a sex category. This is not arbitrary, but based on socially agreed and – for cisgender people – reliable biological criteria. However, those criteria could have been otherwise, for instance using a broader range of biological features and more than two categories. Also the supposedly biological male/female sex category quickly takes on a social role that is independent of genitals and operates even when they are hidden.