I've never seen right wingers talk badly about Clinton due to her gender. I've heard plenty of talk on almost every single other one of her traits, but I think the progressives in the US are a bit to quick to pull out the sexism/racism card.
I don't think the sexism/racism shouts from progressives at Trump (and his supporters) were related to conservatives' disapproval of Clinton. The folks that voted for Trump did so not because they are sexist; they did it because they just plain hated Clinton (in particular) and the establishment.
I don't think the majority of Trump voters actually believe that Clinton shouldn't be president because she's a woman. They just view her as a corrupt, establishment politician and Trump just seemed like the lesser of two evils in their eyes.
I think the media vastly underreported just how much the Right hates Clinton. The Right wing media has been pushing anti-Clinton rhetoric hard for about eight years now!
Eight years? More like 20+. I was a kid in the 90s but still remember how much people plain hated the Clintons. Things like Waco and the Assault Weapons Ban drove them absolutely nuts. Like with Hillary's emails, the Clintons' shady behavior made everything so much worse than whatever they actually did.
/E these articles say everything better than I could. They were written in the early 2000s.