They do, but there are enough conservatives who really hate women that I don’t think we’ll see a female Republican nominee for a long time. VP again, sure, but look at how a lot of people talked about Nikki Haley. She’s plenty authoritarian and a ton of them hated her.
She’s a rat, the fat is just making her head look shorter than it is.
(Also, for anyone concerned about abuse, she has a disorder that causes her to get fatty tissue deposits, she’s not obese.)