All understanding is predicated on what we can observe and comprehend. Objectivity depends on who has the power to say what is objective and what is subjective. Likewise, unless you are dealing with specific mathmatical concepts everything is at is heart subjective to human understanding and ability to measure (even quantum theory). Yes, this is a post-modern conception of science, but it does not demolish the scientific method; rather, it enables us to better understand that culture, political perspectives, and any other axis of society impact how we do science and how that science is presented.

Gender identity is subjective based on culture, point in history, language used, religious belief, legal system, up bringing, economic structures, I could go on. That in English we have settled on a binary construct for gender does not mean that it is anything other than the subjective understanding handed down over the course of English etymology.