Gender informs and shapes most of our conceptual and gender-related opinions about our friends and relatives as well as their everyday roles.
To imagine one's father as a female drastically changes one's perception of him as an individual, since the word father itself, implies certain male or manly attributes, characteristics and traits. Similarly, to imagine one's mother as a male would radically influence one's perception of her 'core person' or individuality since some of her intrinsic qualities as a human being are linked to her sensibility as a woman.
While the mental experiment of turning one's male friends into females and one's female friends into males is amusing at best, it doesn't reveal true or false answers to such vexing questions about someone's 'core personality'.