> it's often the cognitive aspect that challenges the autistic

Yes, that perfectly matches my experiences.

I have far too much affective empathy, but struggle with cognitive empathy and often unintentionally make enemies because I am too clumsy with my words and social interactions, and can't properly gauge social roles (such as when a person looks up to me and would be hurt to hear any criticism from me.)

It stings me when people repeat that I have no empathy at all, and I wish this was better understood by others. Thank you for pointing it out so eloquently.

(Only speaking for myself here, not others! All of us are very different.)