To me, it seems that the reason she is considered stupid is her voice.
It’s not solely because she’s conservative because there are other slanders for conservatives besides the “stupid” label. If the stupid label didn’t stick, liberals would move onto the other labels, such as evil or extremist or zealot.
Actually, the whole meme is built upon a paradoy of her, not the actual person. Pure Alinsky: form a paridigm based on parody and then attack the paradigm, not the person.
Repeat it often enough and people will confuse the two to the point they can't tell what is reality and what is parody.