Women and our interests have always been associated with conservatism, it seems. The concept of 'pearl clutching' is an allusion to women being offended over modern and liberal sensibilities.
I suspect this is because whenever men want to reduce the damage of their rape and violence, they don't know how to do it outside of highly restrictive societal construction. As they are incentivised to ignore the root of the problem, they will always 1. project it onto women, 2. deflect with scapegoats, and 3. create strict social rules in the hope that they can at least make the violence happen elsewhere, or have it hidden from view, so they don't have to look bad, or feel bad, about what they are doing to women en masse.
Conservatives, for example, oppose pornography because they, like the pornographers, believe that sex 'corrupts' women, and they don't want their own female relatives to be corrupted. Meanwhile, feminists oppose pornography because of the material violence committed by men against women within it. But men cannot percieve that women have our own reasoning, so they assume we must align with the male 'conservative' viewpoint. They do the same thing the conservatives do and deflect a male problem - belief that sex, interchangeable with rape, is sinful - onto women, who recognise that there is a difference between consent and rape and simply wish to not be raped.
Women's recognition of moral horrors and our desire to minimise them/be shielded from them is considered 'pearl clutching' because men do not take our claims or morality seriously. They have decided that the violence is a necessary evil, and that morality is not simply a recognition of material harm, but some ethereal and symbolic 'greater good'. The horrific damage caused by men is a nuisance that must be stratified and organised. When this damage is criticised by women, it is understood to be a roundabout way of addressing the same concerns that the conservative man has - and the very fact that women care about actual harm, and therefore we have an emotional investment in the topic, is used as further proof that we are frivolous, unserious, and incapable of making the hard decisions required for leadership. Men, you see, already know that their violence is a problem, and conservativism has its ideological solutions, so everything women say and get upset about is not only redundant but either hysterical or manipulative. The idea that women simply care is never taken into account - because we're all raised to conceptualise the world from a male point of view.
Men have said that prostitution is bad because it corrupts women, so 'swerfs' must secretly agree. Men have said that maleness and femaleness are inherent essences and that the 'feminisation' of society will cause its downful, so 'terfs' must secretly agree. Women are denied a voice at every turn, always assumed to be parroting a much more emotional, manipulative and hysterical version of what men have always said.