I think you're just proving my point. She never could convince people that the accusations against her were false in the same way that Obama was able to do it. And that's because people believe Obama while they didn't believe her. It's because Obama was engaging to listen to while Hillary isn't. Charisma and likability matter. Despite being accused of being a racist that "pals around with terrorist", he came out clean as can be. And those are some very serious accusations. Especially the terrorism links given the political climate at the time.
As far as that gif goes, that's really just her supporters trying to make it important like the Obama gif from one of his older rallies. The difference is that it was true in the case of Obama. He really didn't just brush things off with ease. Hillary never could.
Fox News certainly didn't let it go for the first 3-4 years of Obama's administration. The claim that this simply "went away" and he came out "clean" is false. And comparing the two things isn't exactly fair or accurate, either. Obama had to beat back an ugly story from one dude in his past that he hadn't spoken to in decades, but that was it.
Hillary had to tout around Bill's baggage, because it was her job, apparently, to answer for her husband's administration, despite her not holding office at the time. She always looked guilty by association because of what
he did. Hillary was packaged as "The Clintons," and so many people conflated what Bill's presidency did with her own achievements.
There
is sexism in that. And when you tie that ugly bow on that ugly package, it gets dirty and personal. The problem wasn't that Hillary couldn't "shake off" scandal -- it was that no one would ever
let her. She said over and over again that she wasn't Bill's handler and that his administration was not hers, and nobody cared because
she never did her wifely duty to step in and stop him. Hillary didn't have the luxury of going, "I haven't talked to him in years" the way Obama did.
I'm not entirely sure that even an extremely charismatic woman could've just dropped all of her husband's baggage, just like that. Especially not a woman with a 30-year GOP smear campaign behind both her
and her husband. People on the very young end of the Millennial spectrum (under 25) don't remember the 90s and didn't realize that a lot of what she was being dragged for were Bill's administrative decisions and scandals, not hers. I mean, hell, Sarah Palin was originally seen as a very, very charismatic woman, and even Republicans tore her to shreds. (Deserved, maybe, but not in the way it happened. Being labeled as a "stupid woman" is always disgusting.)
You could use this as an argument as to why maybe Hillary shouldn't have run, but you can't say that "charisma" is the reason why she couldn't convince people that she was innocent. Charisma would've helped, but those ghosts from the past would've haunted her for the rest of her political life no matter what.