I don't think you're quite understanding me. I'm not saying the "gender binary is real," I am saying that gender as a social expression of one's felt sense of self is real. The identification of oneself as gender nonconforming is a real, social aspect. Race is not. The social relations we all have are material processes. Capitalism is a material process. It sounds like you are dangerously close to suggesting trans identity is idealist, but this is fundamentally incorrect. I know you aren't directly saying this, and that you do support trans identity, but without a grounded understanding of dialectical materialism, we cannot understand how social relations function.

Using capitalism as an example, capitalism is a material social relation. You cannot directly point to capitalism, just like you cannot point to gender or nation, but these all involve concrete relations between people. This is not idealism, where we see ideas as prior to matter, but instead relations between people as concrete processes. Race is not real, it is a bourgeois theory that attempts to draw hard lines between peoples that do not exist. Ideology is another excellent example of the relation of ideas to matter:

Ideology, in this context, refers not just to philosophy or ideas, but to a profoundly material force which exists in the practices, rituals and institutions of civil society; institutions such as the education system, the family, the church and the media.

I also recommend the work of Harry Haywood on the question of "race" vs. Nation in the context of Black Statesians.