Hypothetical question for you - I don't relate this to the woman in the OP at all.
I remember seeing kids do this all the time when I was that age: So lets say you're behind a school bus and a kid flips you off from the back window. You respond in kind and also flip him off in response.
A 2nd kid in the bus recorded you and now shared it on social media. You become identified - Should you be fired from your job?
If I am a school teacher, definitely. Otherwise, it will matter a whole lot on my boss. If they felt it reflected poorly on the business, I would expect so. I have seen people fired for less. I once witnessed a UPS driver get fired for wearing black socks (dress code requires brown.)
But note, this was not just an encounter on some random street caught on social media. This was at the school she worked at, and to a parent of one of the kids that attend that school. If I flipped someone off in my offices parking lot, and that person happened to be a customer, who then complained to my boss? Yes, I would expect I would be fired. Just as a boss I would probably fire someone under those conditions.