There's a bunch here that I don't agree with, but rather than TL;DR and start a whole bunch of tangents all at once, I will say that one point we agree on is that Hillary's gender was a negative factor in this election for multiple reasons. What stands out to me in retrospect is that the most common reason I heard given for people opposing/disliking her was that she wasn't "honest and trustworthy"... but I ask, what politician is honest and trustworthy? We universally view politicians as dishonest and untrustworthy, so giving that as your main beef with Hillary rings false... It's kind of like saying you dislike a football player because he is "big and muscular". I think the "dishonest and untrustworthy" reason/excuse for opposing Hillary is a pretty good suspect for a "placeholder" for some other less PC or some less clever/thoughtful/fair-sounding motive... it doesn't necessarily have to be gender specifically and certainly not only gender, it could be a combination of things, like say being uncomfortable with someone "marrying into power" or her being in a political-royalty class/family, but again, you can see how those are also indirectly connected to gender.
Honesty and trustworthiness aren't common in politicians, but the ability to
appear honest and trustworthy is a critical political skill that Hillary is terrible at. I felt a general sense of untrustworthiness about her even when she was saying things that I know to be true, or that completely aligned with positions she's had throughout her career. It's not rational, but very little about human decision-making is. I'll call it "trustiness" after Colbert's "truthiness". Low-trustiness people seem slimy even when they're not, and high-trustiness people seem trustworthy even when they're crooked. Keeping in mind that most people see the DC political establishment as corrupt anyway, running an untrusty person from the core of the Dem establishment was a poor choice.
Trustiness isn't a female-gendered thing, at least for me and probably for most people. To me, female politicians usually come across as trustier than male ones, but Hillary Clinton is a giant exception to that rule. Her trustiness is so low that many people preferred a known con artist who isn't especially trusty himself.
Most people who say they don't trust Clinton are actually honest both to themselves and other people.
Another example of a major negative toward Hillary I've heard that seems fine coming from liberals, but rings like "placeholder" coming from conservative/Republican-voters, and conservative/Republican leaning moderates... is the "hawk/warmonger" label... because Republican politicians are generally hawks, so for Republican leaning voters to suddenly claim that as a dealbreaker just comes off as a lot of BS, smokescreening for something else.
Republicans generally won't want to cross ranks and vote for a Democrat, so in general you're going to hear all sorts of BS excuses for why they dislike any given Democrat.
However, there is actually a substantial number of anti-war Republicans these days. Having local people come back in body bags from a nonsense war actually did change the views of a lot of Republican voters. Anti-war Republicans are generally isolationist, America-first types who might favor a large military for defense but who want to stay out of foreign wars, including defending US allies. Trump played to this group masterfully - notice how much he hammered on first his primary opponents and then Clinton for the Iraq War and Libya. Of course he supported both of them initially, but he's never let the truth stop him. He even went on to suggest not defending our distant allies against attack, which is an even stronger isolationist view. But in order not to appear soft, he also announced his strong support of torture, family-killing, and other war crimes against terrorists. Still, opposing Clinton-McCain style hawkishness is actually a common GOP position.
So I guess the point is that gender is a factor. I think that if Tulsi Gabbard (or whoever) runs... in order to be successful, she is going to have to be attractive enough of a candidate to overcome the gender factor. Obama did this, and the way he did it, is highlighted by a comment that you keep making... describing him as having/talking "in a normal American accent" and going as far as to qualify that successful candidates would need to fit into a narrow "Obama-like" category. That "Obama-like" characteristic that you describe, is precisely what enabled some people to see past his lack in the other essential categories. Connecting this principle back to female candidates for POTUS... essentially you're implying that a woman (or whatever) can be successful as long as they aren't too stereotypically representative of their group, ostensibly in a way that makes it too difficult for people to forgive their lack of proper categories. Another way of saying it, is that as long as you act enough like you are in the proper categories, the fact that you aren't actually in them, can be overlooked.
I completely agree with all of this.
I'm not saying that that race and gender are not huge factors, I'm saying that I don't see it in general election returns. What I think is going on is that would-be politicians who do not fit into the mold of acting and sounding like a "middle-to-upper-class straight white Christian male", except that they happen to be [disadvantaged group X] are filtered out as possible politicians long before they ever become serious contenders for office. People are perfectly fine with voting for someone who agrees with them ideologically and who has all the same traits they do, even if they look different. It's when they deviate from the norms of the dominant culture that the othering begins.
I say the "Obama-like" thing not because I agree that it's the way things should be, but because it's true. As I'm sure you know far better than I do, most white people treat minorities who show all the signs of being part of the dominant culture (accent, dress, teeth, and on and on - it's a long list) similarly to how they treat other white people. Not identically, but pretty close. Then they pat themselves on the back for being so tolerant. Likewise, the most successful female politicians are ones who display traits we associate with men. Whatever else someone may think of them, people rarely fault Thatcher, Merkel, Indira Gandhi, or Golda Meir for being weak. Hillary is actually from this mold too - note that she is accused of hawkishness, a trait usually associated with men. She just has a few critical flaws (bad public speaking, low trustiness, establishment politician in anti-establishment election) that brought her down.
It's a very unequal playing field, but most people are (technically) telling the truth when they say they would vote for women or racial minorities, just not some specific one. In the case of women specifically, while their gender is a barrier to advancing in politics, there are very few people who won't vote for a woman whose political views and overall style match their preferences. Practically none of the people who were chanting "Trump That [lady dog]" wouldn't vote for Ann Coulter in a heartbeat. It wouldn't make them not misogynists or that gender doesn't matter, it just means that even most crypto-fascists will vote for certain women.
