Firstly, Ms Mensch is not “rebranding feminism in her own image”, but writing about how she approaches feminism. Tory feminism is no more Louise-feminism than it is Clara-feminism. We all have our own individual perspective.
Secondly, some women don’t see themselves as victims because they aren’t victims. Yes, as you point out, some women are beaten and abused. But while I sympathise with these women wholeheartedly as human beings, I don’t think I have any special connection to them simply because we share an x-chromosome. People do terrible things to other people, and women are statistically more likely to suffer. I recognise the collective nature of discrimination, but it is because discrimination is collective that a collective fightback fails. Collective politics pits one side against another, entrenching and separating, feeding the cycle of distrust and misunderstanding. The pragmatic response to collective discrimination is to demonstrate that discrimination is ridiculous because we are individuals.
Thirdly, being reluctant to ban something does not mean supporting it. Ms Moore says that “if everything is left to a deregulated market, then everybody is up for sale”. Not quite: if everything is left to a deregulated market then it is up to society to say what is up for sale. Tory feminism knows the problem of female representation in the media – but they want to use society and public opinion to change it, not legislation.
(* While I disagree with much of Ms Moore’s article, this is likely to be due to ideological approaches, and she certainly writes a coherent and measured response to Ms Mensch. Here is an example of a response which is neither coherent nor measured.)