Yep, she was "mouthing off". How stereotypical, both from a sexist and racist point of view.
Minimising someone's experience and telling them how they could've handled it (when they didn't ask you if they handled it well or not) or else, they get no understanding from you IS ridiculous.
She was not at a "shop". It wasn't a random incident involving a shopkeeper and a random Jane Public. She is not you, so how you claim you'd react is irrelevant.
Even so, many people do go on social media, mumsnet, etc to report what they believe to be unfair treatment received from shops, etc and I very much doubt you'd say "jack" to any of them, especially if it was a woman speaking against a man.