On top of what is said in the other comment (indeed, "gender" is perfectly fine, there is no real confusion), it's also worth noting that the "more aggressive" and "more nurturing" sparrows have a different color, and color is a biological trait.

I think that the distinction between "biological" and "cultural" is a bit of a non-issue for the professionals. They don't know if it's cultural or biological, but it does not matter, and in fact, the reality is probably that untangling cultural from biological is impossible (not in the sense that the culture is a direct result of the biology, but in the sense that biological development does not care to make the distinction if the conditions that shape its direction are biological or cultural, and that a final trait is therefore the result of a complicated mix of the two).