You know how to short-circuit this and make them self-destruct? Own it, then flip it around. Don't deny it. If she literally says "you're a pedophile then!" you respond with "yup, I sure am. I also think killing people is wrong. So if you agree that murder is wrong, you support pedophilia. Now either go start shooting people outside or get your sister's tight little buns in here!"
I'm not kidding. Do it in front of others who feel uncomfortable around her, too. The more "witnesses" the better, because watching the looks on her face as her brain tries to unscramble the utter horseshit she's just prompted will make you fucking die of laughter. It's such an over-the-top exaggeration that it's implausible (even if she desperately wants to believe you're a pedophile, her cognitive dissonance will cheerfully point out "hey dumbass, they never fucking admit it" and the chaos in her mind just starts building up from there as the rest of it starts to peel like an onion for her). Nobody else who hears it will believe that part of your statement. But the rest makes the flaw in her logic obvious -- even bad people often hold agreeable opinions, so automatically opposing obviously good ideas because the wrong person emits them is fucking stupid, and this makes it plain by exaggerating it.
