More evidence that low levels of hostile sexism predict sexism against men

In this post, I discussed the possibility that "persons at the lower levels of hostile sexism are nontrivially persons who are sexist against men". Brian Schaffner provides more information on this possibility, in the paper "How Political Scientists Should Measure Sexist Attitudes". I'll place Figure 2 from the paper below:

From the paper discussion of Figure 2 (p. 14):

The plot on the right shows the modest influence of hostile sexism on moderating the gender treatment in the politician conjoint. Subjects in the bottom third of the hostile sexism distribution were about 10 points more likely to select the female profile, a difference that is statistically significant (p=.005). However, the treatment effect was small and not statistically significant among those in the middle and top terciles.

From what I can tell, this evidence suggests that the proper interpretation of the hostile sexism scale is not as a measure of sexism against women but as a measure of male/female preference, with participants who prefer men sorted to high levels of the measure and participants who prefer women sorted to low levels of the measure. If hostile sexism were a proper linear measure of sexism against women, low values of hostile sexism would predict equal treatment of men and women and higher levels would predict favoritism of men over women.