2. Latent sexism.
To be clear, I'm not suggesting that the people who respond badly to Holdo are themselves raging sexists who affirmatively believe that women are inferior. Rather, I think they're more likely falling victim to, and failing to realize the impact of, the sexism in society at large. The first response for many when seeing Holdo in charge is "Who the hell is this?!" From that flows pretty much every other criticism of her character, from being high-handed and needlessly secretive, to her being rude or mean or whatever. It's all based on this underlying notion that she doesn't belong in that position. It's not even a conscious notion, really, and it sits right alongside everyone absolutely accepting (for example) that Leia is running the entire Resistance. No problem there. But that doesn't mean it isn't coming as a result of sexism.
The way I see it, try a little thought exercise. Take Laura Dern out of the film, replace her with, say, Idris Elba or Bruce Greenwood or Brian Cox or (etc., etc., etc.), and ask yourself if you'd really have a problem with the character. You don't have to answer me, but I'm betting that a lot of people, if they're being honest, would probably have a lot less of a problem with any of these actors in that role. That's sexism. Not conscious, "go make me a sammich" sexism, but unconscious discomfort at a woman (A) being in a role traditionally held by a man (or a fish-man), and (B) talking down to a man, especially one who has previously proven himself in combat (even if he also proved himself to be a fool in his last sortie). Again, I am not saying that you're some kind of woman-hating knuckle-dragging MRA red-pill blogger. I'm saying that your response is a kind of conditioned response borne of the sexism inherent in our society, and that's exactly why having roles like Holdo are important: they break that sort of thing down.
You know what the ideal response to a character like Holdo should be?
Nothing. Nothing whatsoever. Nobody bats an eye at it, whether Holdo is a woman, a man, a fish-man, a fish-woman, or whatever. It shouldn't matter at all. But because we live in a sexist society, when people try to push back against that, it sticks out and folks respond. Which, to me, proves that there needs to be more challenging of those kinds of norms, because they're arbitrary, artificial, and wholly unnecessary.