To repeat: From my own experience (and I have followed feminist arguments for a long time), I do not remember ever reading a feminist using this experiment to argue that all observed behavioural differences between men and women are based on socialisation.
I have, however, read many anti-feminists (sex essentialists), at least, arguing that the experiment proved that gender roles and gender stereotypes are based on biology, i.e., that male people will always do things a certain way and that female people will always do things a certain way. These are the people who believe in male supremacy, in women's roles to stay at home and so on.
So I saw it used NOT as a feminist argument but as an anti-feminist argument: That 'gender' is hard-wired into sexed brains.
Recently I have seen it used by trans activists to argue that gender identity is immutable and built in from birth. Those interpret David as possessing an abstract male gender identity so he would have been 'cis' in their ideology who was forced to transition against his will.
Here, too, gender (in the sense of identity) is hard-wired, but may not be in the correctly sexed body (from their point of view).
So overall the feminists, in my experience, were the least likely to use this study to defend anything, while both male supremacists of the old type (far right) and the new type (TRAs) have used it to defend their own philosophies.