The guy is a douche bag. Clearly said "Young man". Anyone looking at that kid thinking she is a he at first glance needs their eyes checked. I don't know why he said "young man", but I don't think it matters. He's claiming he said "young ma'am". I'm doubting that.
Kid most definitely doesn't know what Infowars is. Her reaction was purely to being called a man.
I don't like her reaction, or the fact that her immediate response, after swearing at the guy, was to snap his picture, flip the bird, and walk off. It's one thing to raise kids that are confident. It's another (much easier task) to raise an asshole.
I see this as a bigger problem. IMHO, too many people walk around "not giving a fuck" about anything, including how they treat others.
Actually, I agree with you - change my mind - overall: ashamed.
I think the guy is a total DB and was clearly looking to throw her off. However, she didn't need to 'one-up' the level of poor conduct and could have handled it in a much more clever way... But, at least she didn't demure and "let it go" or pretend she didn't hear him call her "Man". So she get's some points for that. But it was an opportunity lost and, as someone mentioned here, she'll need to learn to handle herself better as she grows up.