There aren't too many places on Wall Street that offer union protection; it's not like she will have a shop steward arguing on her behalf anytime soon.
In any event, it wouldn't matter; all of the employment agreements in the private sector are crystal clear that employment is "at will". And if it sounds harsh that one's stupidity outside of the job could get him or her fired, there are certain types of behavior that reflect an absolutely abysmal lack of judgment.
Someone sliding down a railing at a football game went over the side and fell on top of someone in the next level; he was fired from his position within days of the incident. deadspin.com
That he was enjoying the day off on his own time meant nothing to his employer.
Most at will employers have written policies which govern terminations. And yes, that can cover behavior outside employment which can impact the employers reputation. Note 79, they reference racism as the reason for not termination, but putting her on administrative leave pending investigation. 27, 58, 69, 74, 86 all reference the bird watchers behavior before the video, in his own words. She may well have felt threatened, certainly her dog was. If all their is is describing the black man who threatened her as black to the 911 operator, I'd speculate she'll be back at work. You're right, she won't have a shop steward arguing her case, likely an attorney who might love to pursue the case.