You are right that it's often tactically the wrong decision to post about an ongoing dispute. I will give you that. I'd be surprised if any attorney would recommend for her to post on Quora about the termination while the suit was ongoing.
However, this one-sided "professionalism" whereby people are expected to keep the secrets of employers who fuck them over is disgusting. That expectation exists because there's a power relationship, and because society really hasn't advanced much out of the Dark Ages, and not for any good moral reason.
In Hollywood movies, people like whistleblowers.
Unfortunately, in real life, whistleblowers almost always get a negative reception, even from people who are supposed to be neutral because they have no obvious interest. (People just don't like bad news, full stop.) And the discussion usually gets to a smear against how they are saying it (status reduction) rather than what they are saying. The goal is to create the appearance that: (a) this person didn't go through proper channels, and (b) therefore isn't worth listening to, and (c) deserves various unrelated adverse consequences (such as being blacklisted from future employment) that will make it harder to concentrate from the case at hand.
You're right that her employment opportunities in the future are damaged by this. That's the reality of the world we live in. It shouldn't be that way, but powerful people tend to protect their own.
If there isn't much hard evidence (and in this case, there's not) then people will tend to side with power if they're emotionally rightist and against power if they're emotional leftists. (I'm an emotional leftist, as you can probably tell.)
What you discover when you become a whistleblower is that about 70 percent of people are on the emotional right. They think they're in the center because they don't reject the whistleblower out of hand (instead, they complain that "she may be right, but she didn't use proper channels and I certainly want nothing to do with this matter.") That's not always a bad thing; the powerful entity is known, and the whistleblower is a total unknown, and people tend to be afraid of unknowns. It does, however, make it very difficult to be an effective whistleblower. Worse yet, an even larger percentage of people in positions of power (such as future employers) are on the emotional right.
White-collar employment culture is emotionally rightist in the extreme; if your ex-company says you weren't a leader and you say you were, they're often taken to be right and you're wrong. It's extremely unfortunate and wrong that it's this way, but I don't see how it could be any different (surprise: high-ranking people in powerful institutions tend to side with power) but it is something one needs to be aware of.
This is true, the best solution is normally to go elsewhere and succeed. Whether that means at another company or on your own. People tend to have a lens through which they understand the world, once they have slotted you it is over (see: bozo bit, various cognitive biases, etc...)
1. Employers can treat their employees like crap, not many people seem to be bothered by it. But when a employee says anything even remotely bad, suddenly he/she is unprofessional, immature etc
2. In the case of whistle blowers, we spend more time arguing the behavior of the whistle blower (aka the "correct" way of whistle blowing) than actually looking into the allegations.
So in short, even if I (the whistle blower) have a legitimate case (racism, ageism, sexism...whatever), then I am expected to act totally "professional" if I ever expect to be taken seriously.
I don't have a problem with the fact that she filed the suit. She clearly felt discriminated and harassed enough to file it. It's fine to drop a line to journalists with the unsealed court documents, and build your public opinion case that way.
Just because you don't get the promotion you feel entitled to, doesn't mean you should sue your employer for discrimination.