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 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!
/E these articles say everything better than I could. They were written in the early 2000s.
Edit: just Google image search "Trump that bitch" and tell me again gender has nothing to do with it.
1) his hair
2) his (supposed) psychological state, e.g. [1]
3) "deplorables" - we all know what and who is meant by this and very few or none of these are responsible for their situation
4) his family name
I like how Dilbert's author put it. This is why Trump won [2], or, more humorously [3]
[1] http://www.theatlantic.com/magazine/archive/2016/06/the-mind... [2] http://blog.dilbert.com/post/152293480726/the-bully-party [3] https://www.youtube.com/watch?v=sb7XaRPFPjI https://www.youtube.com/watch?v=WVKC0egDBpk and https://www.youtube.com/watch?v=dvpDwtYl5TA