It’s projection. Fox and other right-leaning news outlets have always run a lot of stories about pedophilia compared to media outlets with a center or left bias. Some people find it titillating, then use rage about the injustice to mask their feelings to others and to themselves. It speaks to right-wing fantasies of power and control, and they can justify hours looking at child-porn-adjacent material as “research”. To be clear the exploitation of children is a true moral outrage, but there’s a reason that so much time is spent on “research” versus concrete action in the offline world. On a larger scale, it’s no coincidence that 4chan and 8chan are the source of QAnon - both were created to skirt censorship of child porn and racist ideology. Misdirecting outrage about the exploration of children in the direction of the ideological left provides cover.
I don’t think every right-winger is a secret pedophile, by the way, but I do think that most engage in similar fantasies of power, domination, and control. Many right-wingers are feeling powerless - and shamed - right now, so the fantasy of being a righteous soldier for the exploited innocents fits the bill.