Is the presidency so inherently alpha that any female candidate would be "unlikeable"?
I think you're wrong here.
Female candidates in general would face all kinds of opposition and protest that male candidates would not, but "unlikeable" is not really a general anti-feminist trait as exhibited by those with misogynist tendencies.
If Elizabeth Warren were the nominee, she would be attacked for being a bleeding-heart liberal (there go those gals wanting everyone to have health care, hugs, bunnies and rainbows), but not for being unlikeable. Take somebody a bit out of left field, like say Caroline Kennedy - again she is not unlikeable and my guess is they would attack her for being an entitled princess or some similar thing Rush would come up with.
Hillary is uniquely unlikeable in my opinion. She has a tendency to come across as really, really smug, which is interesting because I see Obama as more professorial and intellectual which a certain segment of society hates, but he (mostly) manages to not come across like he is irritated to be explaining something to the masses yet again. She also comes across as a liar in the sense that she would be willing to do or say whatever it takes - plenty of examples of male politicians who also change their votes whichever way the wind blows. Hell Trump is a much bigger liar and has been branded so.
None of this in any way justifies voting for Trump, but I think that we're really trying to twist ourselves into a pretzel here to explain away Hillary's faults as somehow being the inherent fault of a sexist electorate. Sorry, there is plenty there to dislike without any misogyny. I have many, many highly educated feminist (some even ultra-feminist) friends, not a single one of them thinks much of her, though would all vote for her given the alternative.