A lot of Red Pill thought centers around the biological differences between the two genders, while transhumanism centers around transcending biological limits - including those imposed by gender differences - through the use of technology.

Suppose we suddenly stumbled upon some sort of magical technological breakthrough, tomorrow, that allowed people to transfer their minds into robots/computer simulations/whatever and essentially allow themselves to define their physical form as whatever they feel represents themselves the best.

Would this invalidate the idea that the personality differences between people of each gender is completely down to sexual dimorphism? Why or why not?