My observation is that there are certain standards which are illegal for a company to use as the basis for firing someone.
For example, a company may not fire someone based on marital status. Even if there is a company policy that only single people may be employed at a company. Nor may an accountant be fired for wearing a yarmulke at work; some workplace religious practices being another protected policy.
These don't even need to be Title VII violations. It is illegal for a company (at least in Colorado, which is where this company is located) to fire a janitor who, in off-hours, enjoys being a street mime, that being a 'lawful activity off the premises of the employer during nonworking hours' and doesn't fit any of the exceptions to the law.
So just saying that something is unprofessional and against company policy, doesn't mean that that is lawful basis for firing someone, because acting on that policy can be illegal.
I think you agree with that. (I'm setting up for the next part.) Your view is instead that "the fact that she represented her company in an unprofessional manner that led to her being fired."
The problem is that the law doesn't appear to allow the company to use this form of unprofessional behavior as the basis for firing someone.
If it did, then any act that a company disagreed with, while done during company time, would be illegal. For example, under the NLRA a company may NOT "prohibit you from wearing union hats, buttons, t-shirts, and pins in the workplace except under special circumstances", even if you are on company time, representing the company, and the company policy says that wearing your union pin is "unprofessional."
The law is very clear that there are things that a company may not use as grounds for firing. Reporting sexual harassment is a protected action, public discussion of sexual discrimination in industry or at a workplace is also a protected action, public shaming of one's employer for allowing discriminatory practices is a protected action. This is well settled by the courts.
Now the Title VII protections only apply so long as every reasonable person would say that there was justification to believe there was discriminatory act, even if this belief ends up being false. The court cases I read are very careful to point out that employees aren't expected to know the law and that some actions, while apparently discriminatory on the surface, are actually not. Even in those cases, an incorrect claim of discrimination may not be used as the basis for firing someone.
Making false accusations is not covered by this law. An employee cannot make false claims about sexual harassment while at the workplace and expect to be protected under Title VII or similar laws. So it's not like this is a safe harbor for spreading lies and misinformation.
To conclude, where in all the laws and court cases that allow someone to make a private report of sexual harassment, without fear of reprisal through firing, does it say that making a public report of sexual harassment is not also protected? Because I can't find it even after several hours of research.