no one has really supported the OP's claim that misogyny directed against conservative women is 'acceptable',
but unacceptable against any other sort of women.
That's mostly because the thread has focused on politicians, famous individuals, and other non-Conservative women. The true hatred towards Conservative women in society has to do with the stay-at-home-moms, the homemakers, the non-working wives, and those women who have chosen a truly Conservative, Traditional lifestyle.
THOSE are the women that the media, the feminists, the civil rights activists, and others berate and deride. The gender war's version of "Uncle Toms"; who have chosen to side with the "enemy" of modern women..... the human male; in the battle of the sexes.
THOSE are the women that are constantly abused by society for their choice in life. A choice which would have been their only significant option less than a century ago. Yet to make that same choice now is "abandoning the sisterhood" as I've heard it refered to more than once.
So don't tell me that Conservative women aren't treated less well in our society than Liberal/Feminist women are. I'm not even sure you can make that arguement with a straight face.