How does accepting both of these somehow invalidate the belief that gendered behavior is mostly social or learned?
All knowledge of these objects, what they're used for, and who uses them were learned from societal influences. A kid doesn't have to care about social norms to tell that most people they see playing with sticks or driving dump trucks are men, and most people they see pushing strollers and playing with dolls are women. It's like that from out in the park to within picture books.
Asserting that there are sex-based personality differences is not incompatible with gendered behavior being mostly social or learned.