Honestly kind of curious: are furious and infuriated not synonyms for you?
I really was curious! But that isn't mutually exclusive with skepticism.
I think "furious", the more I think of it, is an anger regarding lack (ie if someone's house gets vandalized and the feel a loss in property value). Curiosity could culminate with inquisitiveness, which functionally feels like adopting new beliefs. Skepticism can culminate with dismissiveness. So as long as you're open to the possibility that your mind could be changed, it counts as curiosity, I suppose.