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.
Local candidates usually have websites, do interviews with local papers, and are suuuper excited to talk to potential voters, so people could look at any of that?