How would you respond to This woman who was fired for voicing her opinion at work?

She wasn't a private employee, but a federal employee working for a federal court. Rules are different for government employees. As far as First Amendment protection goes, normally speech of a government employee as a private citizen on matters of public concern is protected, but can be weighed against whether there are overriding public interests. In this case, the judge who fired her seems to believe that the impartiality of the court was at risk and that was sufficient to justify terminating her employment.

Note that she is afforded that protection only because she spoke as a private citizen outside of work; had she made the same statement as part of her duties (and not as a private citizen), the government could have disciplined or fired her regardless.

The situation is different in the NFL, which is primarily about labor law and not freedom of speech/expression. NFL players are unionized, so the employers (i.e. the owners) cannot unilaterally change the terms of employment without involving their union.

Also, the protection granted by section 7 of the NLRA for speech as part of protected concerted activities is very broad. While such activities have to be for work-related reasons, kneeling to oppose employer policy on forcing employees to stand would seem to fall under those.

Finally, First Amendment concerns may arise here, anyway, as the government (via the sitting president) chose to get involved and tried to exert pressure on the NFL to implement such a policy. When the government deputizes private actors, those private actors become state actors and become subject to respecting (inter alia) First Amendment rights. Whether the NFL was actually acting on behalf of the government in this sense would have to be decided by a court, of course.