Your first sentence is spot on.
The rest? I don't think people hater her for being a woman as much as for all the stench that the GOP has covered her with for two decades now. She has been a main target of the GOP for a long time and it's working well for them.
Was anyone reading the Wall Street Journal back in the 1990's when they had their 6 volume "exposé" of the Whitewater dealings the Clinton's had been involved with? Boy, they absolutely HATED the Clintons. I pretty much quit reading their opinion pages then. They haven't had a good thing to say about any President since Reagan.