Aren't biology/culture intrinsically linked to theology by virtue of the Incarnation and the fact that salvation history happens to real, biological human beings placed in real cultures and contexts in history?

Far Eastern religions/philosophies propose what you are proposing that theology is essentially divorced from the actual drama of human history as it unfolds across real people's lives and cultures. Judaism and Christianity claim the opposite in that God reveals Himself precisely in and through real people's specific lives and cultures to bring about the salvation of all people.

Do you really want to make the claim that gender has no actual theological significance?